Inclusion Criteria:  Has histologically or cytologically confirmed diagnosis of ES-SCLC in need of second-line therapy Has progressed on or after treatment with an anti-programmed cell death 1 (PD-1)/ programmed cell death ligand 1 (PD-L1) monoclonal antibody (mAb) administered as part of first-line platinum-based systemic therapy for ES-SCLC Has ES-SCLC defined as Stage IV (T any, N any, M1a/b/c) by the American Joint Committee on Cancer, Eighth Edition Has received 1 prior line of systemic therapy for small cell lung cancer (SCLC) Male participants must be abstinent from heterosexual intercourse or agree to use contraception during treatment for at least 7 days after the last dose of lenvatinib. No contraception is required if the participant is receiving pembrolizumab, pembrolizumab/quavonlimab, MK-4830, or favezelimab/pembrolizumab Female participants are not pregnant or breastfeeding and are not a woman of childbearing potential (WOCBP) or if are a WOCBP, are abstinent from heterosexual intercourse or are using contraception during the intervention period and for at least 120 days after the last dose of pembrolizumab, pembrolizumab/quavonlimab, MK-4830, or favezelimab/pembrolizumab or 30 days after the last dose of lenvatinib, whichever occurs last A WOCBP must have a negative highly sensitive pregnancy test (urine or serum as required by local regulations) within 24 hours before the first dose of study treatment Has measurable disease per RECIST 1.1 as assessed by local site investigator/radiology and verified by BICR Has submitted an archival tumor tissue sample or newly obtained core, incisional, or excisional biopsy of a tumor lesion not previously irradiated Has an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 assessed within 7 days before allocation/randomization Participants who are Hepatitis B surface antigen (HBsAg) positive are eligible if they have received Hepatitis B virus (HBV) antiviral therapy for at least 4 weeks and have undetectable HBV viral load before randomization Participants with history of Hepatitis C virus (HCV) infection are eligible if HCV viral load is undetectable at screening Has adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP ≤150/90 millimeters of mercury (mm Hg) with no change in antihypertensive medications within 1 week before allocation/randomization Has a predicted life expectancy of >3 months  Exclusion Criteria:  Has had major surgery within 3 weeks before first dose of study treatment Has a preexisting ≥Grade 3 gastrointestinal or non-gastrointestinal fistula Has clinically significant cardiovascular disease or major arterial thromboembolic event within 12 months before first dose of study intervention, including New York Heart Association Class III or IV congestive heart failure, unstable angina, myocardial infarction, cerebral vascular accident, or cardiac arrhythmia associated with hemodynamic instability Has active hemoptysis (bright red blood of at least 0.5 teaspoon) within 3 weeks before the first dose of study treatment Has gastrointestinal malabsorption or any other condition that might affect oral study intervention absorption Has serious nonhealing wound, ulcer, or bone fracture within 28 days before the start of study treatment Has any major hemorrhage or venous thromboembolic events within 3 months before the start of study treatment Has a history of inflammatory bowel disease Has a history of a gastrointestinal perforation within 6 months before the start of study treatment Has a known history of, or active, neurologic paraneoplastic syndrome Has received prior therapy with a receptor tyrosine kinase (RTK) inhibitor or anti- cytotoxic T-lymphocyte-associated protein 4 (CTLA-4), anti-immunoglobulin-like transcript (ILT)-4, or anti-lymphocyte-activation gene 3 (LAG-3) agents Has received prior therapy with an anti-PD-1/L1 agent and was permanently discontinued from that treatment due to a treatment-related adverse event Has received prior systemic anticancer therapy including investigational agents within 4 weeks before start of study treatment Has received prior radiotherapy within 2 weeks of start of study treatment Has received lung radiation therapy >30 Gray (Gy) within 6 months before the first dose of study treatment Has received a live or live attenuated vaccine within 30 days before the first dose of study treatment Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks before the first dose of study treatment Has radiographic evidence of encasement or invasion of a major blood vessel, or of intratumoral cavitation Has symptomatic ascites, pleural effusion, or pericardial effusion 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 the first dose of study treatment Has a known additional malignancy that is progressing or has required active treatment within the past 3 years Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Participants with brain metastases may participate only if they satisfy all of the following: completed treatment (e.g., whole brain radiation treatment, stereotactic radiosurgery, or equivalent) ≥14 days before the first dose of study intervention; have no evidence of new or enlarging brain metastases confirmed by post-treatment repeat brain imaging (using the same modality) performed ≥4 weeks after pretreatment brain imaging; and are neurologically stable without the need for steroids for ≥7 days before the first dose of study intervention as per local site assessment. Participants with untreated brain metastases will be allowed if they are asymptomatic, the investigator determines there is no immediate CNS-specific treatment required, there is no significant surrounding edema, and the brain metastases are of 5 millimeter (mm) or less in size and 3 or less in number. Has a history of severe hypersensitivity reaction (≥Grade 3) to any study treatment and/or any of its excipients Has an active autoimmune disease that has required systemic treatment in past 2 years (ie, with use of disease modifying agents, corticosteroids or immunosuppressive drugs) Has a history of (noninfectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease Has an active infection requiring systemic therapy Has a known history of Human Immunodeficiency Virus (HIV) infection Has concurrent active HBV or HCV Has progressive disease as initial response to first-line systemic chemotherapy in combination with PD-1/L1 inhibitor for ES-SCLC Has had an allogenic tissue/solid organ transplant