Inclusion Criteria:
1. Be able and willing to sign a written informed consent form before taking part in the study.
2. Be 18 years of age or older.
3. Have a confirmed diagnosis of metastatic non-small cell lung cancer (NSCLC), established by examination of a tumor tissue sample, with cancer that has spread to distant parts of the body.
4. Have a confirmed RET gene rearrangement, identified using a validated molecular test, such as next-generation sequencing (NGS), polymerase chain reaction (PCR), fluorescence in situ hybridization (FISH), or another validated method.
5. Have previously received treatment for metastatic NSCLC and have experienced disease progression during or after at least one previous line of standard systemic chemotherapy or targeted therapy.
6. Have previously received platinum-containing chemotherapy for metastatic NSCLC and have experienced disease progression during or after this treatment.
7. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1, meaning that the participant is fully active or able to perform light daily activities.
8. Have at least one tumor lesion that can be measured on imaging according to the Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST 1.1).
9. Have an expected life expectancy of at least 3 months.
10. Have adequate blood cell counts at screening, defined as:
* absolute neutrophil count of at least \\(1.5 \\times 10\^9/L\\);
* platelet count of at least \\(100 \\times 10\^9/L\\);
* hemoglobin level of at least 90 g/L.
The participant must not have received a blood transfusion or transfusion of blood components within 14 days before starting study treatment.
11. Have adequate liver function at screening, defined as:
* total bilirubin no higher than 1.5 times the upper limit of normal (ULN); participants with Gilbert syndrome may have a total bilirubin level up to 3 times the ULN;
* aspartate aminotransferase (AST) and alanine aminotransferase (ALT) levels below 3 times the ULN; for participants with liver metastases, levels below 5 times the ULN are allowed;
* alkaline phosphatase (ALP) level below 3 times the ULN; for participants with liver and/or bone metastases, a level below 5 times the ULN is allowed.
12. Have adequate kidney function at screening, defined as:
* serum creatinine no higher than 1.5 times the ULN; or
* creatinine clearance of at least 50 mL/min if the serum creatinine level is higher than 1.5 times the ULN.
Creatinine clearance will be calculated according to local medical standards. If no local standard is available, it may be calculated using the Cockcroft-Gault formula. Estimated glomerular filtration rate (eGFR) may also be used instead of serum creatinine or creatinine clearance, according to the study protocol.
13. Have a thyroid-stimulating hormone (TSH) level within the normal range at screening. At the investigator's discretion, a participant with a TSH level outside the normal range may still be eligible if the triiodothyronine (T3) and free thyroxine (free T4) levels are within the normal range.
Exclusion Criteria:
1. They have previously received treatment with lenvatinib.
2. They have had a severe allergic or hypersensitivity reaction to pembrolizumab, lenvatinib, any component of the study medicines, or similar medicines, including human, humanized, or mouse monoclonal antibodies or immunoglobulin medicines.
3. They have an active autoimmune disease.
4. They have cancer that has spread to the central nervous system or has caused carcinomatous meningitis. Participants with brain metastases may be eligible if the brain metastases were adequately treated with radiation therapy and/or surgery and have remained stable on imaging studies.
5. They have a clinically significant heart condition, including uncontrolled high blood pressure, coronary artery disease or any type of angina, a previous heart attack or post-heart-attack heart damage, or heart failure classified as New York Heart Association (NYHA) class II or higher.
6. Imaging or clinical examination shows that the tumor has invaded blood vessels or is located close to major blood vessels, and the investigator believes that this could increase the risk of bleeding.
7. They have severe kidney or liver failure.
8. They have any known allergy to an ingredient in the study medicines.
9. They are pregnant or breastfeeding.
10. They have uncontrolled high blood pressure despite treatment, defined as systolic blood pressure above 150 mmHg and/or diastolic blood pressure above 100 mmHg. Participants with a hypertensive crisis or hypertensive encephalopathy are also excluded.
11. They have another serious medical condition that, in the investigator's opinion, could affect participation in the study or the safety of the participant.
12. They have ongoing side effects from previous treatment that are more severe than Grade 1.
13. Women who could become pregnant are not willing to use an effective method of contraception during the study and for at least 30 days after the last dose of the study medicines.
14. Men with partners who could become pregnant are not willing to use an effective method of contraception during the study and for at least 30 days after the last dose of the study medicines.
