Inclusion Criteria:
1. Aged \>=18 years
2. For Dose-Escalation: Females (TNBC, EC and OC) or males/females (NSCLC, adenocarcinoma). Participants with the following disease characteristics:
Participants with the following tumor types, each as a separate arm:
1. TNBC: Histologically confirmed diagnosis of metastatic TNBC (that is, estrogen receptor (ER) negative/progesterone receptor negative/ human epidermal growth factor receptor 2 (HER2) negative (defined as immunohistochemistry (IHC) less than (\<) 2 plus (+) or fluorescence in situ hybridization (FISH) negative) breast cancer). Previously treated with at least one line of systemic anticancer therapy (cytotoxic or targeted anticancer agents) in the metastatic setting.
2. NSCLC adenocarcinoma: Histologically or cytologically confirmed metastatic NSCLC adenocarcinoma: participants who have failed previous treatment for metastatic disease, are not indicated or failed epidermal growth factor receptor (EGFR)-, Anaplastic lymphoma kinase (ALK) -, B-Raf proto-oncogene (BRAF) - or c-ros oncogene 1 (ROS1) - targeted therapy, and for whom no alternative standard therapy exists.
3. EC: Histologically confirmed diagnosis of advanced, recurrent or metastatic EC. Relapsed or failure of at least one platinum-based regimen or one immunotherapy-based regimen.
4. OC or primary peritoneal cancer or fallopian tube cancer: Histologically confirmed diagnosis of high grade serous epithelial ovarian cancer or primary peritoneal cancer or fallopian tube cancer.
Participants must have:
* platinum-resistant disease (defined as progression within 6 months after the last dose of at least 4 cycles of the last platinum containing chemotherapy regimen)
* received up to 4 lines of systemic therapy post development of platinum resistance.
For Dose-Confirmation and Dose Optimization:
Note: Only participants with histologically confirmed diagnosis of advanced, recurrent, or metastatic EC will be enrolled at sites in France.
High-grade serous ovarian cancer or primary peritoneal cancer or fallopian tube cancer:
* Platinum-resistant disease:
* For participant with 1 line of platinum-containing therapy: progression greater than (\>) 1 month and less than or equal to (\<=) 6 months after the last dose of the first platinum-containing chemotherapy regimen (of at least 4 cycles)
* For participant with 2-3 lines of platinum-containing therapy: progression during or within 6 months after the last dose of the 2nd or 3rd platinum-containing chemotherapy regimen.
* Have received up to 3 prior lines of systemic therapy and for whom single-agent therapy is appropriate as the next line of therapy. Participants may have been treated with up to one line of therapy subsequent to determination of platinum-resistance. In Dose Optimization Part B participants may have received up to 3 prior lines of systemic therapy, up to 4 prior lines is permitted for participants who have received prior mirvetuximab soravtansine
* Neoadjuvant plus/minus (±) adjuvant will be considered 1 line of therapy.
* Maintenance therapy (example, bevacizumab, PARP inhibitors) will be considered part of the preceding line of therapy (will not be counted as an independent line of therapy).
* Hormonal therapy will be counted as a separate line of therapy unless it was given as maintenance.
* Therapy changed due to toxicity in the absence of progression will be considered part of the same line.
Endometrial cancer (not enrolled in Dose Optimization Part B):
* Participants must have histologically confirmed diagnosis of advanced, recurrent, or metastatic EC. All histologic (including carcinosarcoma \[no more than one participant at any dose level\]) and molecular subtypes will be included. Participants may have been treated with an Immune Checkpoint Inhibitor (ICI) containing regimen (or be ineligible for ICI treatment) and must have had no more than 2 prior regimens (not including adjuvant therapy if progression or recurrent/metastatic disease occurred more than 6 months after the completion of the last cycle of adjuvant therapy).
* Note: There is no restriction regarding prior hormonal therapy.
3. Available tumor tissue for FRA expression percent (%) by IHC analysis as assessed at a central laboratory. There is no minimum requirement for FRA expression (%). However, the tumor sample must be evaluable for IHC analysis (that is, of sufficient quality with adequate tumor content). Sample resubmission will be permitted for participants with tissue result of "non-evaluable" who are otherwise eligible. Tumor sample submission must be archival formalinfixed, paraffin-embedded (FFPE) tissue block, or unstained slides sectioned within 45 days from the latest FFPE block, or a fresh biopsy sample obtained during screening but prior to initiation of study treatment. Participants who have received prior treatment with mirvetuximab soravtansine will be required to provide a fresh biopsy sample during screening.
4. Radiological disease progression on or after the most recent therapy by investigator assessment.
5. Measurable disease meeting the following criteria (confirmed by central radiographic review, in the Dose-Confirmation Part only):
* At least one lesion of \>1.0 centimeter (cm) in long axis diameter for non-lymph nodes or \>1.5 cm in short axis diameter for lymph nodes that is serially measurable according to Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 using either computed tomography (CT) or magnetic resonance imaging (MRI),
* Lesions that have had external beam radiotherapy (EBRT) or loco-regional therapies such as radiofrequency (RF) ablation must show evidence of PD based on RECIST 1.1 to be deemed a target lesion.
6. ECOG PS of 0 or 1.
7. Participants who are expected to survive a minimum of 3 months after the first administration of the study drug.
8. Adequate renal function as evidenced by serum creatinine less than or equal to (\<=) 1.5 milligram per deciliter (mg/dL) or calculated creatinine clearance \>=50 milliliter per (mL) /minute according to a 12 or 24 hour urine collection.
For Dose Optimization Part B, adequate renal function as evidenced by calculated creatinine clearance \>=50 milliliters per minute (mL/min) by Cockcroft-Gault formula.
9. Adequate bone marrow function, as evidenced by:
* Absolute neutrophil count (ANC) \>=1.0\*10\^9 per liter (/L) (MORAb-202 monotherapy cohorts only)
* ANC \>=1.5\*10\^9/L (MORAb-202 plus lenvatinib cohorts)
* Hemoglobin (Hgb) \>=9.0 gram per deciliter (g/dL)
* Platelet count \>=75\*10\^9/L Growth factors or transfusions as per institutional practice, are allowed if needed to achieve the above values. Growth factor and platelet transfusion should not be used within 7 days of initiation of study treatment.
10. Adequate liver function, as evidenced by:
* Total bilirubin \<=1.5\*upper limit of normal (ULN) except for unconjugated hyperbilirubinemia (example, Gilbert's syndrome)
* Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \<=3\*ULN (in the case of liver metastases \<=5\*ULN). Participants with Alkaline Phosphatase (ALP) \<=3\*ULN unless they and are known to have bone metastases in which case higher ALP values will also be allowed.
* Albumin \>3.0 g/dL.
11. Participants must undergo a washout period required from the end of prior treatment to the first administration of the study drug that will be as follows:
Prior anticancer therapy:
* Prior chemotherapy, surgical therapy, radiation therapy: \>3 weeks. Prior chest radiotherapy or pneumonectomy is an exclusion.
* Antibody and other biologic therapeutic agents: \>=4 weeks.
* Endocrine therapy or, small-molecule targeted therapy: \>2 weeks.
* Immunotherapy \>=4 weeks.
12. Participants with a history of deep vein thrombosis (DVT) within 3 months of enrollment must be on a stable dose of anticoagulation as demonstrated by appropriate laboratory parameters (depending on the anticoagulant agent) for a minimum of 2 weeks before to starting study treatment. Anticoagulation must continue while on study treatment.
13. Participants at risk for DVT secondary to central venous catheters or with past medical history of DVT or clinical symptoms suggestive of DVT must have venous Doppler ultrasonography to rule out DVT during the screening period and before to initiation of study treatment.
14. If a participant has undergone major surgery, the participant must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment.
15. Resolution of anticancer therapy-related or radiation-related toxicities to Grade 1 severity or lower, except for stable sensory neuropathy (Grade \<=2), anemia (\[haemoglobin\] Hgb \>=9.0 g/dL), and alopecia (any grade).
16. Participant must be willing and able to comply with all aspects of the protocol.
17. Participant must provide written informed consent prior to any study-specific screening procedures.
18. For cohorts where MORAb-202 is used in combination with lenvatinib: Has adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP \<=150/90 millimeter of mercury (mm Hg) and no change in antihypertensive medications within 1 week before the first administration of the study drug.
Exclusion Criteria:
1. Participants with endometrial leiomyosarcoma, endometrial stromal sarcoma or other soft tissue sarcoma histology.
2. Participants who received previous treatment with any folate receptor targeting agents, except for mirvetuximab soravtansine in the setting of FRA \>=75%.
3. Participants with platinum refractory ovarian cancer (defined as disease progression during the initial platinum-based chemotherapy treatment).
4. Currently enrolled in another clinical study or used any investigational drug or device, which in the opinion of the Sponsor may interfere with the study treatment, within the past 28 days or 5 times the half-life (where prior drug therapy falls under the parameters these Inclusion Criteria should be followed) of any investigational drug preceding informed consent.
5. Participants with brain or subdural metastases are not eligible, unless they have completed local therapy and have discontinued the use of corticosteroids for this indication for at least 2 weeks before starting treatment in this study. Brain metastases must be stable for at least 4 weeks on 2 consecutive scans of the brain before starting study treatment.
6. Diagnosed with meningeal carcinomatosis.
7. Any other invasive malignancy that required treatment (other than definitive surgery) or has shown evidence of recurrence/progression (except for non-melanoma skin cancer, or histologically confirmed complete excision of carcinoma in situ) during the 2 years prior to starting study treatment.
8. Significant cardiovascular impairment. History within 6 months prior to the first dose of study drug of: congestive heart failure greater than New York Heart Association (NYHA) Class II); unstable angina; myocardial infarction; stroke; cardiac arrhythmia associated with hemodynamic instability.
In addition, for participants enrolled in the MORAb-202 plus lenvatinib cohorts, significant cardiovascular impairment also includes: History of arterial thromboembolism within 12 months of starting study treatment; Left ventricular ejection fraction (LVEF) \<50% or below the institutional normal range determined by multigated acquisition scan (MUGA) or echocardiogram (ECHO).Note: Medically controlled arrhythmia is permitted.
9. Clinically significant ECG abnormality, including marked prolonged baseline QT as corrected using Fridericia's formula (QTcF) (repeated demonstration of a QTcF interval \>500 milliseconds \[ms\]). A history of risk factors for torsade de pointes (example, heart failure, hypokalemia, family history of long QT Syndrome) or the use of concomitant medications that prolong the QTcF.
For participants enrolled in the MORAb-202 plus lenvatinib cohorts, prolongation of the QTcF interval to \>480 ms.
10. Known to be Human Immunodeficiency Virus (HIV) positive. Testing at entry not required.
11. Active viral hepatitis (B or C as demonstrated by positive serology). Testing at entry if there are no symptoms or history is not required unless as per local requirements.
12. Females who are breastfeeding or pregnant at Screening or Baseline (as documented by a positive beta human chorionic gonadotropin \[ß-hCG\] or human chorionic gonadotropin \[hCG\]) with a minimum sensitivity of 25 International units per liter (IU/L) or equivalent units of ß-hCG \[or hCG\]. A separate baseline assessment is required if a negative screening pregnancy test was obtained more than 72 hours before the first administration of the study drug.
13. Females of childbearing potential who
* within 28 days before study entry, did not use a highly effective method of contraception, which includes any of the following:
* total abstinence (if it is their preferred and usual lifestyle)\*
* an intrauterine device or intrauterine hormone-releasing system (IUS)
* a contraceptive implant
* combined (estrogen and progestogen containing) hormonal contraception associated with inhibition of ovulation (oral, intravaginal, transdermal) or progestogen-only hormonal contraception associated with inhibition of ovulation (oral, injectable, implantable). Participants using an oral contraceptive (participant must be on a stable dose of the same oral contraceptive product for at least 28 days before dosing and throughout the study and for 7 months (5\*half-life plus 180 days) after study drug discontinuation)
* bilateral tubal occlusion
* have a vasectomized partner with confirmed azoospermia
* do not agree to use a highly effective method of contraception (as described above) throughout the entire study period and for 7 months (5\*half-life plus 180 days) after study drug discontinuation.
For sites outside of the EU, it is permissible that if a highly effective method of contraception is not appropriate or acceptable to the participant, then the participant must agree to use a medically acceptable method of contraception, that is, double-barrier methods of contraception such as latex or synthetic condom plus diaphragm or cervical/vault cap with spermicide. NOTE: All females will be considered to be of childbearing potential unless they are postmenopausal (amenorrheic for at least 12 consecutive months, in the appropriate age group, and without other known or suspected cause) or have been sterilized surgically (that is, bilateral tubal ligation, total hysterectomy, or bilateral oophorectomy, all with surgery at least 1 month before dosing).
\*Sexual abstinence is considered a highly effective method only if defined as refraining from heterosexual intercourse during the entire period of risk associated with the study intervention. The reliability of sexual abstinence needs to be evaluated in relation to the duration of the study and the preferred and usual lifestyle of the participant.
14. For Dose-Escalation only: Males who have not had a successful vasectomy (confirmed azoospermia) or they and their female partners do not meet the criteria above (that is, not of childbearing potential or practicing highly effective contraception throughout the study period and for 7 months (5\*half-life plus 180 days) after study drug discontinuation). If the female partner is pregnant, then males who do not agree to use latex or synthetic condoms throughout the study period and for 4 months (5\*half-life plus 90 days) after study drug discontinuation. No sperm donation is allowed during the study period and for 4 months (5\*half-life plus 90 days) after study drug discontinuation.
15. Pulmonary Function Test (PFT) abnormalities: FEV1/FVC \<0.7, FEV1 or FVC \<80%, DLCO \<80% or less than the lower limit of normal according to local institutional standards.
16. Current ILD/pneumonitis, or ILD/pneumonitis is suspected at Screening or history of interstitial lung disease (ILD)/pneumonitis of any severity including ILD/pneumonitis from prior anticancer therapy.
17. Current infectious pneumonia, history of viral pneumonia (including COVID-19-related infection) with evidence of persistent radiologic abnormalities.
18. Lung-specific clinically significant illnesses including, but not limited to any underlying pulmonary disorder (example, pulmonary embolism), asthma, chronic obstructive pulmonary disease (COPD), and restrictive lung disease, or currently receiving any medication that is associated with a clinically significant risk of developing ILD.
19. Clinically significant pleural or pericardial effusion requiring drainage or ascites requiring peritoneal shunt.
20. Prior pneumonectomy.
21. History of chest radiotherapy. Participants with history of chest wall radiation (example, history of breast cancer) may be permitted if chest wall radiation is documented \> 2 years before starting study treatment.
22. Any autoimmune, connective tissue, or inflammatory disorders (example, rheumatoid arthritis, Sjögren's syndrome, sarcoidosis, etc) where there is documented (or suspicion of) pulmonary involvement.
23. A known history of active TB (bacillus tuberculosis).
24. Scheduled for surgery during the study, other than minor surgery which would not delay study treatment.
25. An active clinically significant (in the opinion of the Investigator) infection requiring systemic therapy within 2 weeks prior to the first dose of study drug.
26. Administration of a live, attenuated vaccine within 4 weeks prior to the first dose of study drug, or anticipation that such a live attenuated vaccine will be required during the study. Inactivated vaccines (such as hepatitis A or polio vaccines) are permitted during the study. Seasonal influenza and COVID-19 vaccines that do not contain live virus are permitted.
27. Any prior hypersensitivity to monoclonal antibodies or contraindication to the receipt of corticosteroids or any of the excipients (investigators should refer to the prescribing information for the selected corticosteroid).
28. Known intolerance to either of the components of the study drug.
29. Any medical or other condition which, in the opinion of the investigator would preclude the participants participation in the clinical study.
30. Receiving any medication prohibited in combination with the study treatment(s) as described in the product label for eribulin, unless medication was stopped within 7 days prior to enrollment.
31. Known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.
Dose Optimization Part B participants who receiving MORAb-202 in combination with lenvatinib:
32. \>1+ proteinuria on dipstick, 24-hour urine protein is \>=1 gram.
33. Gastrointestinal malabsorption or any other condition that might affect the absorption of lenvatinib.
34. Unable to take oral medication.
35. Major surgery within 3 weeks before the first dose of study treatment. Note: adequate wound healing after major surgery must be assessed clinically and independent of time elapsed for eligibility.
36. Serious nonhealing wound, ulcer or bone fracture.
37. Pre-existing Grade \>=3 gastrointestinal (GI) or non-GI fistula.
38. Radiographic evidence of major blood vessel invasion/infiltration. The degree of tumor invasion / infiltration of major blood vessels should be considered because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis following lenvatinib therapy.
