Study of Pembrolizumab, Lenvatinib and Chemotherapy Combination in First Line Extensive-stage Small Cell Lung Cancer

Inclusion Criteria: \- 1. Histologically or cytologically documented new diagnosis of SCLC by histology or cytology from brushing, washing, or needle aspiration. Note: Subjects who do not have histology samples (defined as core or excisional biopsy, or resections) will need to undergo a new biopsy to provide a tissue sample. Mixed tumors are not eligible. * 2\. ES-SCLC, stage IV disease by the American Joint Committee on Cancer, 8th Edition criteria (70), \[T any, N any, M1a, M1b, M1c\], or T3-4 due to multiple lung nodules that are too extensive or tumor/nodal volume that is too large to be encompassed in a tolerable radiation plan. * 3\. Have at least one lesion that meets criteria for being measurable, as defined by RECIST 1.1. * 4\. Have provided archival tumor tissue sample or newly obtained core or excisional biopsy of a tumor lesion not previously irradiated for biomarker assessment. * 5\. Be male or female ≥18 years of age inclusive, on the day of signing informed consent. * 6\. Have a life expectancy of at least 3 months from the study start. * 7\. Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 within 7 days prior to the first dose of study intervention. * 8\. Male participants are eligible to participate if they agree to the following during the intervention period and for at least 30 days after the last dose of lenvatinib placebo and up to 180 days after the last dose of chemotherapeutic agents: * Refrain from donating sperm PLUS either: * Be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis) and agree to remain abstinent OR * Must agree to use contraception unless confirmed to be azoospermic. \- 9. A female participant is eligible to participate if she is not pregnant or breastfeeding, and at least one of the following conditions applies: * Is not a WOCBP OR * Is a WOCBP and using a contraceptive method that is highly effective * 10\. Have voluntarily agreed to participate by giving written consent for the study prior to any specific protocol procedures. * 11\. Have adequate organ function Exclusion Criteria: * 1\. Has received any prior therapy (chemotherapy, radiotherapy, surgical resection) or other investigational agent for the treatment of SCLC. * 2\. Is expected to require any other form of antineoplastic therapy for SCLC, including radiation therapy while on study. * 3\. Active CNS metastases and/or carcinomatous meningitis as determined per CT or MRI during screening. Participants with previously treated brain metastases (eg, whole brain radiation treatment \[WBRT\], stereotactic radiosurgery, or equivalent) may participate only if they satisfy the following: * Completed treatment at least 14 days prior to the first dose of study intervention. * Are clinically stable, without requirement of steroid treatment for at least 7 days prior to first dose of study intervention. * Are radiologically stable. * Patients with new asymptomatic CNS metastases detected at the screening scan must receive radiation therapy and/or surgery for CNS metastases. Following treatment, these patients may then be eligible without the need for an additional brain scan prior to enrollment, if all other criteria are met. * 4\. Has received prior therapy with an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent or with an agent directed to another stimulatory or co-inhibitory T-cell receptor (eg, CTLA-4, OX-40, CD137). * 5\. Spinal cord compression not definitively treated with surgery and/or radiation or previously diagnosed and treated spinal cord compression without evidence that disease has been clinically stable for ≥ 1 week prior to enrollment. * 6\. Uncontrolled pleural effusion, pericardial effusion, or ascites requiring recurrent drainage procedures (once monthly or more frequently). A subject who is clinically stable following treatment for these conditions (including therapeutic thoraco- or paracentesis) is eligible. * 7\. .Has known history of, or active, neurologic paraneoplastic syndrome of autoimmune nature. * 8\. Radiographic evidence of intratumoral cavitations, encasement, or invasion of a major blood vessel. Additionally, the degree of proximity to major blood vessels should be considered for exclusion because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis after lenvatinib therapy. * 9\. Has had major surgery within 4 weeks prior to first dose of study interventions. * 10\. Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of trial drug. * 11\. 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 the first dose of study intervention. * 12\. Has an active autoimmune disease or inflammatory disorder that has required systemic treatment in the past 2 years. * 13\. Has a diagnosis of immunodeficiency or is taking chronic systemic steroid therapy (in dosing of \>10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment. * 14\. Has known history of a second malignancy other than SCLC, unless potentially curative treatment has been completed with no evidence of malignancy for at least 3 years since the initiation of that therapy. * 15\. Poor controlled hypertension (BP\>150/90 mmHg) despite appropriate treatment. * 16\. Participants with proteinuria \>1+ on urine dipstick testing/urinalysis will undergo 24-hour urine collection for quantitative assessment of proteinuria. Participants with urine protein ≥1 g/24 hours will be ineligible. * 17\. Has a prolongation of QTc interval (calculated using Fridericia's formula) of \>480 msec. * 18\. Has a known history of interstitial lung disease, idiopathic pulmonary fibrosis, organizing pneumonia (e.g., bronchiolitis obliterans), drug-induced pneumonitis, idiopathic pneumonitis, or evidence of active pneumonitis on screening chest CT scan * 19\. Uncontrolled intercurrent active infection at the time of enrollment requiring systemic therapy. * 20\. Has a known history of Human Immunodeficiency Virus (HIV) infection. * 21\. Has a known history of Hepatitis B or known active Hepatitis C. * 22\. Has a known history of active tuberculosis. * 23\. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study. * 24\. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * 25\. Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study. * 26\. Prior allogeneic bone marrow transplantation or solid organ transplant. * 27\. Any gastrointestinal condition that would affect the absorption of Lenvatinib. * 28\. Has active hemoptysis or major arterial thromboembolic event within 2 weeks prior to the first dose of study intervention. * 29\. Has significant cardiovascular impairment within 12 months prior to the first dose of study intervention. * 30\. Has a history of a severe (Grade ≥ 3) hypersensitivity reaction to treatment with another monoclonal antibody or has a known hypersensitivity to lenvatinib, pembrolizumab, carboplatin or etoposide and/or any of its excipients. * 31\. Has a clinically active diverticulitis, inflammatory bowel disease, intra-abdominal abscess, gastrointestinal obstruction and/or abdominal carcinomatosis. * 32\. Has a history of a gastrointestinal perforation within 6 months before the first dose of study intervention. * 33\. Has preexisting Grade ≥ 3 gastrointestinal or non-gastrointestinal fistula. * 34\. Has serious nonhealing wound, ulcer, or bone fracture within 28 days before first dose of study intervention. * 35\. Has any major hemorrhage or venous thromboembolic events within 3 months before the first dose of study intervention. * 36\. Poor medical risk due to a serious, uncontrolled medical disorder or nonmalignant systemic disease.