A Study of Pembrolizumab With Lenvatinib in Women With Advanced Uterine Carcinosarcoma

Inclusion Criteria: * Histologically confirmed persistent/recurrent uterine or ovarian carcinosarcomas. For this study, a histological diagnosis of carcinosarcoma must include identifying high grade malignant epithelial and mesenchymal components. The mesenchymal component can be homologous or heterologous. * Patients with known microsatellite stable (MSS), microsatellite instability high (MSI-H), mismatch repair proficient (pMMR) and mismatch repair deficient (dMMR) uterine or ovarian carcinosarcoma are eligible. * Patients must have had 1 prior platinum-based chemotherapy regimen and could have received up to 3 prior lines of systemic therapy. * All chemotherapy must have been completed at least 3 weeks prior to the start of study therapy * Hormonal Therapy will NOT count as prior treatment line. * All hormonal therapy for treatment of endometrial or ovarian carcinosarcomas must be discontinued at least one week prior to start of study therapy. * Prior Bevacizumab also allowed and must be at least 3 weeks prior to the start of study therapy. * Prior Parp-inhibitors also allowed and must be at least 3 weeks prior to the start of study therapy. * Age ≥18 years at the time of informed consent * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months of registration are eligible for this trial. * participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: * Not a WOCBP as defined in Appendix B or * A WOCBP who agrees to follow the contraceptive guidance in Appendix B during the treatment period and for at least 120 days after the last dose of study treatment(s) (MK and or any active comparator/combination) plus 30 days (a menstruation cycle) for study treatments with risk of genotoxicity\] after the last dose of study treatment. * The participant (provides written informed consent for the study. * Have an Eastern Cooperative Oncology Group ECOG performance status of 0 or 1. * Have adequate organ function. Assessments must be collected within 7 days prior to the start of study treatment. * Adequate Organ Function Laboratory Values Hematological * Absolute neutrophil count (ANC) ≥1500/μL * Platelets ≥100 000/μL * Hemoglobin ≥9.0 g/dL Renal * Creatinine clearance (CrCL) or estimated Glomerular filtration rate (GFR) CrCL of ≥51 mL/minute estimated using either the Cockcroft-Gault equation, a 24 hour urine test or another validated test as per local Practice (e.g., estimated GFR): Estimated CrCL = (140-age \[years\]) × weight (kg) × 0.85 serum creatinine (mg/dL) × 72 Hepatic * Total bilirubin ≤1.5 ×ULN (patients with known Gilbert's disease who have bilirubin level ≤ 3 x ULN may be enrolled) * AST, ALT, and ALP ≤3 × ULN (≤5 × ULN for participants with liver metastases)3 Thyroid * TSH TSH within normal limits (TSH \<ULN allowed in euthyroid patients on thyroid replacement therapy) * At least 1 measurable target lesion according to RECIST 1.1 including the following: Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Non-nodal lesion that measures ≥1.0 cm in the longest diameter * Lymph node (LN) lesion that measures as ≥1.5 cm in the short axis * The lesion is suitable for repeat measurement using computed tomography/magnetic resonance imaging (CT/MRI). Lesions that have had external beam radiotherapy (EBRT) or locoregional therapy must show radiographic evidence of subsequent growth. * Adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP ≤150/90 mm Hg at screening and no change in antihypertensive medications within 1 week before C1D1. Exclusion Criteria: * 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). * Has received prior therapy with a VEGF TKI to include but not limited to: lenvatinib, lucitinib, cederinib, and cabozantonib * Has participated in a study of an investigational agent and received cancer directed study therapy within 4 weeks prior to start of study treatment. Note: Participants must have recovered from all AEs due to previous therapies to ≤Grade 1 or baseline. Participants with ≤Grade 2 neuropathy may be eligible. Note: If participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting study treatment. * Has received prior radiotherapy within 2 weeks of start of study treatment. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. * Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed. * 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 the first dose of study drug. * Steroids as CT scan contrast premedication is allowed * The use of inhaled or topical corticosteroids is allowed * The use of mineralocorticoids (e.g., fludrocortisone) for patients with orthostatic hypotension or adrenocortical insufficiency is allowed. * Has a known additional malignancy that is progressing or has required active treatment within the past 2 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g. breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded. * Has known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study treatment. * Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. * Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. * Uncontrolled intercurrent illness including, but not limited to: ongoing or active infection (except for uncomplicated urinary tract infection), interstitial lung disease or active, noninfectious pneumonitis, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/substance abuse/social situations that would limit compliance with study requirements. * Has known clinically significant liver disease, including active viral, alcoholic, or other hepatitis; and cirrhosis. For patients with evidence of chronic hepatitis B (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Patients with a history of hepatitis C (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable viral load. * Has a known history of active TB (Bacillus Tuberculosis). * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. * Gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of lenvatinib. * Has a pre-existing Grade ≥3 gastrointestinal or non-gastrointestinal fistula. * Radiographic evidence of major blood vessel invasion/infiltration. The degree of tumor invasion/infiltration of major blood vessels should be considered because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis following lenvatinib therapy. * Clinically significant hemoptysis or tumor bleeding within 2 weeks prior to the first dose of study drug. * Significant cardiovascular impairment within 12 months of the first dose of study drug: such as history of congestive heart failure greater than New York Heart Association (NYHA) Class II, unstable angina, myocardial infarction or cerebrovascular accident (CVA) stroke, or cardiac arrhythmia associated with hemodynamic instability. * Has had an allogenic tissue/solid organ transplant. * Known intolerance to study treatments (or any of the excipients). * Participants with proteinuria \>1+ on urine dipstick testing will undergo 24-h urine collection for quantitative assessment of proteinuria. Participants with urine protein ≥1 g/24 h will be ineligible. * Prolongation of QTc interval to \>480 ms. * Left ventricular ejection fraction (LVEF) below the institutional normal range as determined by multigated acquisition scan (MUGA) or echocardiogram (ECHO).