Lenvatinib in Combination With Pembrolizumab Versus Treatment of Physician's Choice in Participants With Advanced Endometrial Cancer (MK-3475-775/E7080-G000-309 Per Merck Standard Convention [KEYNOTE-775])

Inclusion Criteria: 1. Has a histologically confirmed diagnosis of endometrial carcinoma (EC) 2. Documented evidence of advanced, recurrent or metastatic EC. 3. Has radiographic evidence of disease progression after 1 prior systemic, platinum-based chemotherapy regimen for EC. Participants may have received up to 1 additional line of platinum-based chemotherapy if given in the neoadjuvant or adjuvant treatment setting. Note: There is no restriction regarding prior hormonal therapy. 4. Has historical or fresh tumor biopsy specimen for determination of mismatch repair (MMR) status. 5. Has at least 1 measurable target lesion according to Response Evaluation Criteria In Solid Tumors (RECIST) 1.1 and confirmed by Blinded Independent Central Review BICR. 6. Has Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 within 7 days of starting study treatment. 7. Is not pregnant, breastfeeding, and agrees to use a highly effective method of contraception during the treatment period and for at least 120 days (for participants treated with lenvatinib plus pembrolizumab) or at least 180 days (for participants treated with treatment of physician's choice \[TPC\]) after the last dose of study treatment. Exclusion Criteria: 1. Has carcinosarcoma (malignant mixed mullerian tumor), endometrial leiomyosarcoma and endometrial stromal sarcomas. 2. Has unstable central nervous system (CNS) metastases. 3. Has active malignancy (except for endometrial cancer, definitively treated in-situ carcinomas \[e.g. breast, cervix, bladder\], or basal or squamous cell carcinoma of the skin) within 24 months of study start. 4. Has gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of lenvatinib. 5. Has a pre-existing greater than or equal (\>=) Grade 3 gastrointestinal or non-gastrointestinal fistula. 6. Has radiographic evidence of major blood vessel invasion/infiltration. 7. Has clinically significant hemoptysis or tumor bleeding within 2 weeks prior to the first dose of study treatment. 8. Has a history of congestive heart failure greater than New York Heart Association (NYHA) Class II, unstable angina, myocardial infarction, cerebrovascular accident (CVA) stroke, or cardiac arrhythmia associated with hemodynamic instability within 12 months of the first dose of study treatment. 9. Has an active infection requiring systemic treatment. 10. Has not recovered adequately from any toxicity and/or complications from major surgery prior to starting therapy. 11. Is positive for Human Immunodeficiency Virus (HIV). 12. Has active Hepatitis B or C. 13. Has a history of (non-infectious) pneumonitis that required treatment with steroids, or has current pneumonitis. 14. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the study. 15. Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to study start -Has an active autoimmune disease (with the exception of psoriasis) that has required systemic treatment in the past 2 years. 16. Is pregnant or breastfeeding. 17. Has had an allogenic tissue/solid organ transplant. 18. Has received \>1 prior systemic chemotherapy regimen (other than adjuvant or neoadjuvant) for Endometrial Cancer. Participants may receive up to 2 regimens of platinum-based chemotherapy in total, as long as one is given in the neoadjuvant or adjuvant treatment setting. 19. Has received prior anticancer treatment within 28 days of study start. All acute toxicities related to prior treatments must be resolved to Grade ≤1, except for alopecia and Grade ≤2 peripheral neuropathy. 20. Has received prior treatment with any treatment targeting VEGF-directed angiogenesis, any anti-PD-1, anti-PD-L1, or anti-PD-L2 agent. 21. Has received prior treatment with an agent directed to a stimulatory or co-inhibitory T-cell receptor other than an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent, and who has discontinued from that treatment due to a Grade 3 or higher immune-related adverse event. 22. Has received prior radiation therapy within 21 days of study start with the exception of palliative radiotherapy to bone lesions, which is allowed if completed 2 weeks of study start. Participants must have recovered from all radiation-related toxicities and/or complications prior to randomization. 23. Has received a live vaccine within 30 days of study start. 24. Has a known intolerance to study treatment (or any of the excipients). 25. Prior enrollment on a clinical study evaluating pembrolizumab and lenvatinib for endometrial carcinoma, regardless of treatment received. 26. Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks of study start. 27. Participants with urine protein ≥1 gram (g)/24 hour. 28. Prolongation of corrected QT (QTc) interval to \>480 milliseconds (ms). 29. Left ventricular ejection fraction (LVEF) below the institutional normal range as determined by multigated acquisition scan (MUGA) or echocardiogram (ECHO).