Pembrolizumab (MK-3475) Plus Lenvatinib (E7080/MK-7902) Versus Chemotherapy for Endometrial Carcinoma (ENGOT-en9 / MK-7902-001)

Inclusion Criteria: * Has Stage III, Stage IV, or recurrent, histologically-confirmed endometrial carcinoma with disease that is either measurable or nonmeasurable but radiographically apparent, per Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST 1.1) as assessed by blinded independent central review (BICR) (note: may have received prior chemotherapy only if administered concurrently with radiation; may have received prior radiation without concurrent chemotherapy; may have received prior hormonal therapy for treatment of endometrial carcinoma, provided that it was discontinued ≥1 week prior to randomization; and may have received 1 prior line of systemic platinum-based adjuvant and/or neoadjuvant chemotherapy) * Has provided archival tumor tissue sample or newly obtained core or excisional biopsy of a tumor lesion that was not previously irradiated, for determination of mismatch repair (MMR) status * Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1, as assessed within 7 days prior to the first dose of study intervention * Is not pregnant or breastfeeding, and is either not a woman of childbearing potential (WOCBP) or is a WOCBP who agrees to use contraception during the study and for ≥120 days after pembrolizumab, ≥30 days after lenvatinib, or ≥180 days after (chemotherapy) \[if a WOCBP, a pregnancy test will be required within 24 hours of first dose of study drug\] * Has adequately controlled blood pressure within 7 days prior to randomization * Has adequate organ function based on assessment within 7 days prior to the first dose of study intervention Exclusion Criteria: * Has carcinosarcoma (malignant mixed Műllerian tumor), endometrial leiomyosarcoma or other high grade sarcomas, or endometrial stromal sarcomas * Has a central nervous system (CNS) metastasis, unless local therapy (e.g., whole brain radiation therapy, surgery, or radiosurgery) has been completed and have discontinued use of corticosteroids for this indication for ≥4 weeks prior to starting study medication (major surgery within 3 weeks of the first dose of study drug will be exclusionary) * Has a known additional malignancy (other than endometrial carcinoma) that is progressing or has required active treatment in the last 3 years * Has gastrointestinal malabsorption or any other condition that might affect the absorption of lenvatinib * Has a pre-existing Grade ≥3 gastrointestinal or nongastrointestinal fistula * Has radiographic evidence of major blood vessel invasion/infiltration * Has active hemoptysis (bright red blood at ≥0.5 teaspoon) within 3 weeks prior to the first dose of study intervention or tumor bleeding within 2 weeks prior to randomization * Has clinically significant cardiovascular disease within 12 months from first dose of study intervention including New York Heart Association Class III or IV congestive heart failure, unstable angina, myocardial infarction or cerebral vascular accident, or cardiac arrhythmia associated with hemodynamic instability * Has any infection requiring systemic treatment * Has not recovered adequately from any toxicity and/or complications from major surgery prior to randomization * Has a known history of human immunodeficiency virus (HIV) infection (HIV test is required at screening) * Has a known history of hepatitis B (defined as hepatitis B surface antigen \[HBsAg\] reactive) or known active hepatitis C virus (HCV) \[defined as HCV ribonucleic acid (RNA) is detected\] (hepatitis B and C testing is required at screening only when mandated by local health authority) * Has a history of (noninfectious) pneumonitis that required treatment with steroids, or has current pneumonitis * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the participant's participation for the full duration of the study, or is not in the best interest of the participant to participate, in the opinion of the treating investigator * Has a known psychiatric or substance abuse disorder that would interfere with cooperation with the requirements of the study * 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 randomization * Has an active autoimmune disease (with the exception of psoriasis) that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids or immunosuppressive drugs) * Has received prior systemic chemotherapy in any setting for the treatment of endometrial carcinoma (note: prior chemotherapy administered concurrently with radiation is permitted) * Has received prior radiotherapy within 4 weeks prior to randomization (participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis - a 2-week washout is permitted for palliative radiation to non-CNS disease and vaginal brachytherapy) * Has received prior hormonal therapy for the treatment of endometrial carcinoma within 1 week of randomization * Has received prior therapy with any treatment targeting vascular endothelial growth factor (VEGF)-directed angiogenesis, an anti-programmed cell death (PD)-1, anti-PD ligand (L)1, or anti-PD-L2 agent, or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (e.g., CTLA-4, OX 40, CD137) * Has received a live or live attenuated vaccine within 30 days prior to the first dose of study intervention * Has known intolerance to study intervention (or any of the excipients) * Has had an allogenic tissue/solid organ transplant * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks prior to randomization