Inclusion Criteria:
* Group 1 only: Biopsy-proven participants with relapsed or refractory NHL of DLBCL, FL or MZL.
* Groups 3, 4a and 5 only: Biopsy-proven participants with relapsed or refractory DLBCL.
* Groups 2 and 6 only: Biopsy-proven participants with DLBCL and another select lymphoid neoplasms.
* Participants must have at least 1 bi-dimensionally measurable lesion.
* ECOG performance status of 0 to 2.
* Participants with protocol defined laboratory criteria at screening as defined in the protocol.
* Group 1 only:
Received at least 1 previous systemic therapy line for the treatment of NHL. At least 1 previous therapy line must have included a CD20-targeted therapy (eg, RTX).
* Groups 2, 3, 4a and 6 only:
Received at least 1, but no more than 3, previous systemic therapy lines for the treatment of DLBCL. At least 1 previous therapy line must have included a CD20-targeted therapy (eg, RTX).
* Group 5 only: Participants must have:
1. Untreated DLBCL.
2. Ann Arbor Stage III to IV.
3. IPI status of 3 to 5 or age-adjusted IPI 2-3 (in Group 5 only).
4. Appropriate candidate for R-CHOP.
5. LVEF of ≥ 50%, assessed by echocardiography.
* Willingness to avoid pregnancy or fathering children.
* In the opinion of investigator, the participant must:
1. Not have a history of noncompliance in relation to medical regimens or be considered potentially unreliable and/or uncooperative.
2. Be able to understand the reason for complying with the special conditions of the pregnancy prevention risk management plan and give written acknowledgement of this.
Exclusion Criteria:
* Any other histological type of lymphoma.
* History of prior non-hematologic malignancy.
* Congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias.
* Participants with known positive test result for hepatitis C, and hepatitis B.
* Known seropositive for or history of active viral infection with HIV.
* Known active bacterial, viral, fungal, mycobacterial, or other infection at screening.
* Known CNS lymphoma involvement - present or past medical history.
* History or evidence of clinically significant cardiovascular, CNS and/or other systemic disease that would in the investigator's opinion preclude participation in the study or compromise the participant's ability to give informed consent.
* History or evidence of rare hereditary problems of galactose intolerance, Lapp lactase deficiency or glucose-galactose malabsorption.
* History or evidence of interstitial lung disease.
* Vaccination with live vaccine within 21 days prior to study treatment (Note: throughout the study treatment period and at least 6 months after end of treatment, vaccination with live vaccines should be avoided).
* Major surgery within up to 30 days prior to signing the ICF, unless the participant is recovered at the time of signing the ICF.
* Any anticancer and/or investigational therapy within 14 days prior to the start of Cycle 1.
* Groups 2, 3, 4a, 5 and 6 only: Gastrointestinal abnormalities including the inability to take oral study treatment, requiring IV alimentation, or prior surgical procedure affecting absorption.
* Pregnancy or lactation.
* Groups 2, 3, 5 and 6 only: Participants who have history of deep venous thrombosis/embolism, threatening thromboembolism, stroke or known thrombophilia or are at a high risk for a thromboembolic event in the opinion of the investigator and who are not willing/able to take venous thromboembolic event prophylaxis during the entire treatment period if required
* Group 4a only: Use or expected use during the study of any restricted medications, including potent CYP3A4 inhibitors or inducers within 14 days or 5 half-lives (whichever is longer) before the date of study treatment administration
* Groups 1, 3, 4a and 6 only: Participants who have:
1. Not discontinued CD20-targeted therapy, chemotherapy, radiotherapy, investigational anticancer therapy, or other lymphoma-specific therapy within the 14 days prior to Day 1 dosing.
2. In the opinion of the investigator, not recovered sufficiently from the adverse toxic effects of prior therapies.
3. Groups 1, 3 and 4a only: Previous treatment with CD19-targeted therapy (eg, CD19-CAR-T therapies, other CD19 mAbs including bispecific and ADCs).
Groups 2 and 6 only: Previous treatment with tafasitamab. Note: Participants in Groups 2 and 6 who have received previous CD19 directed therapy (other than tafasitamab) must have CD19-positive lymphoma confirmed by a biopsy taken after completing the prior CD19-targeted therapy.
4. Groups 2, 3 and 6 only: Been previously treated with IMiDs (eg, thalidomide or LEN).
5. Group 4a only: Been previously treated with selective PI3Kδ or pan-PI3K inhibitors (eg, idelalisib, copanlisib, duvelisib) and/or Bruton's tyrosine kinase inhibitors (eg, ibrutinib).
6. A history of hypersensitivity to compounds of similar biological or chemical composition to tafasitamab, IMiDs, and/or the excipients contained in the study treatment formulations (citric acid monohydrate, polysorbate 20, sodium citrate dehydrate and trehalose dihydrate).
7. Undergone ASCT within the period ≤ 3 months before the signing of the ICF. Participants who have a more distant history of ASCT must exhibit full hematological recovery before enrolment into the study.
8. Undergone previous allogenic stem cell transplantation.
9. Concurrent treatment other anticancer or experimental treatments.
* Group 5 only: Participants who have:
1. A history of radiation therapy to ≥ 25% of the bone marrow for other diseases or history of anthracycline therapy.
2. A history of hypersensitivity or contraindication to any component of R-CHOP, LEN, or compounds of similar biological or chemical composition as tafasitamab and/or the excipients contained in the study treatment formulations or R-CHOP.
3. Contraindication to any of the individual components of R-CHOP.
4. Any anticancer and/or investigational therapy within 30 days prior to the start of Cycle 1, except for permitted prephase treatment defined below.