Pembrolizumab and Lenvatinib in Clear Cell Ovarian Cancer

Inclusion Criteria: * Participants must have histologically or cytologically confirmed recurrent or persistent clear cell carcinoma of the ovary (CCOC) (≥50% clear cell histology). * Participants must have measurable disease, defined as at least one lesion that can be accurately measured per RECIST v1.1 criteria. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Participants must have received at least one prior platinum-based chemotherapeutic regimen for primary management of disease. * Prior bevacizumab is allowed. * Prior use of immune checkpoint inhibitors (e.g. anti-PD-1, anti-PD-L1, anti-CTLA-4) is allowed for up to 30% of participants. * Unlimited prior lines for the treatment of recurrent or persistent disease are allowed. * Age ≥18 years. Because no dosing or adverse event data are currently available on the use of the combination of pembrolizumab/lenvatinib in participants \<18 years of age, children are excluded from this study. * ECOG performance status of 0 or 1 (Karnofsky performance scale ≥70%). * Participants must have adequate organ and marrow function as defined below: * absolute neutrophil count ≥1,500/μcL * hemoglobin ≥ 9g/dL (without use of erythropoietin; without packed RBC transfusion within preceding 2 weeks) * platelet count ≥100,000/μcL * total bilirubin ≤ institutional upper limit of normal (ULN) (in the absence of liver metastases) or ≤ 1.5 × institutional ULN (in the presence of liver metastases) * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional ULN (in the absence of liver metastases) or ≤5 × institutional ULN (in the presence of liver metastases) * creatinine ≤ 1.5 ×ULN OR glomerular filtration rate (GFR) ≥30mL/min per the CKD-EPI formula for participants with Cr \>1.5×ULN. The CKD-EPI formula is calculated as: GFR = 141 × min (Scr /κ, 1)α × max(Scr /κ, 1)-1.209 × 0.993Age × 1.018 \[if female\] × 1.159 \[if black\] here: Scr is serum creatinine in mg/dL, κ is 0.7 for females and 0.9 for males, α is -0.329 for females and -0.411 for males, min indicates the minimum of Scr /κ or 1, and max indicates the maximum of Scr /κ or 1. * PT/INR, aPTT ≤ 1.5x ULN unless participant is receiving anticoagulant therapy and the PT/INR or aPTT is within the intended therapeutic range of the anticoagulant * Participants must have adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as a BP ≤ 140/90 at screening and no change in antihypertensive medications within 2 weeks prior to Cycle 1 Day 1. * Participants with known brain metastases are eligible if they have completed primary CNS-directed therapy (such as surgical resection or radiotherapy) and if they have remained clinically stable, asymptomatic, radiologically stable without evidence of progression for at least 4 weeks by repeat imaging, and have been off of steroids for at least 4 weeks prior to starting study treatment. * Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen, as determined after discussion with the PI, are eligible for this trial. * Archival tumor tissue must be available as 27 (25 unstained + 2 H\&E) freshly serially cut slides from formalin-fixed, paraffin-embedded (FFPE) tissue blocks. The most recent available tissue is preferred to archived tissue. If fewer than 27 slides are available, the participant may still be eligible pending discussion with the Sponsor-Investigator. * The effects of pembrolizumab and lenvatinib on the developing human fetus are unknown. For this reason and because these agents are known to be teratogenic, women of child-bearing potential\* must have a negative serum or urine pregnancy test at the Screening and Cycle 1 Day 1 visits. Women of child-bearing potential and men must agree to use adequate contraception (see Appendix D) prior to study entry, for the duration of study participation, and for at least 30 days after last receipt of study therapy. Should a woman become pregnant or suspect she is pregnant while she is participating in this study, she should inform her treating physician immediately. \-- Female participants are NOT considered to be of childbearing potential if they meet either criteria: (1) Post-menopausal, defined as amenorrheic for at least 12 consecutive months within the appropriate age group and without an alternative medical cause, OR; (2) Surgically sterilized (i.e. bilateral oophorectomy, bilateral tubal ligation or salpingectomy, or total hysterectomy) * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria * Prior use of lenvatinib. * Use of any immunosuppressive therapy, including steroids used for the purpose of systemic immunosuppression (with dosing exceeding 10mg daily of prednisone or equivalent), within 2 weeks prior to beginning study treatment. The use of steroids as physiologic replacement (e.g. for adrenal or pituitary insufficiency) is allowed. The use of inhaled steroids (e.g. for the treatment of asthma or seasonal allergies) is allowed. The use of prophylactic corticosteroids to avoid allergic reactions (e.g. to IV contrast dye) is allowed. * Anti-cancer treatment (chemotherapy, radiotherapy, or other investigational therapy) within 4 weeks prior to entering the study (6 weeks prior to study entry for nitrosoureas or mitomycin C). * Prior radiation therapy within 2 weeks of start of study drugs. Participants must have recovered from all radiation-related toxicities and must not require steroids. Participants must not have had radiation pneumonitis. Palliative radiation (≤2 weeks of radiotherapy) to non-CNS disease is permitted, provided there is at least a 1-week washout prior to start of study drugs. * Use of herbal supplements, including but not limited to: cannabis, St. John's wort, gingko biloba, ginseng, saw palmetto, and ephedra. Herbal supplements must be stopped at least 1 week prior to beginning study treatment. * Residual toxicities from prior anti-cancer therapy that remain Grade \> 1, with the exception of alopecia and peripheral neuropathy. Toxicities related to prior treatments must have resolved to Grade ≤1 to be eligible. * Has received a live or live-attenuated vaccine within 30 days prior to the first dose of study drug. Administration of killed vaccines are allowed. * Major surgical procedures within 4 weeks of beginning study treatment are not allowed. Minor surgical procedures (with the exception of port placement) within 1 week of beginning study treatment are not allowed. * Subjects having \>1+ proteinuria on urinalysis must undergo a 24-hour urine collection for quantitative assessment of proteinuria. Subjects with urine protein ≥1g/24 hours will be ineligible. * Evidence of bowel involvement. * Any gastrointestinal disorder that would interfere with the passage or absorption of oral medications. Participants must be able to swallow oral medications. Participants with an enteric tube (e.g. gastrostomy or jejunostomy tube), receiving total parenteral nutrition (TPN), or dependent on IV fluid support are ineligible. * Participants with significant cardiovascular impairment, including uncontrolled hypertension, congestive heart failure of New York Heart Association Grade II or above, unstable angina, myocardial infarction within the past 6 months, or serious cardiac arrhythmia within the past 6 months. * Resting corrected QT interval (QTc) interval using the Fridericia formula (QTcF) \>450 ms for males or \>470 ms for females." * Clinically significant bleeding within 4 weeks of beginning study treatment. * Active autoimmune disease requiring systemic treatment (e.g. use of steroids, immunosuppressive medications, or disease modifying agents) within the past 2 years. * Has a diagnosis of immunodeficiency. * Is known to be positive for Human Immunodeficiency Virus (HIV). Subjects with HIV, including those on antiretroviral therapy, are excluded due to risk of immunodeficiency and risk of overlapping hepatotoxicity between antiretroviral agents and lenvatinib. * Is known to be positive for Hepatitis B virus (HBV) or Hepatitis C virus (HCV). Participants are eligible if they have a history of HCV infection that has been treated and cured, with an undetectable viral load. * History of allogeneic tissue/solid organ transplant. * History of non-infectious pneumonitis/interstitial lung disease that required steroids, or has current pneumonitis/interstitial lung disease. * Participants with uncontrolled intercurrent illness, including but not limited to active infection and serious non-healing wounds or ulcers. * Participants with psychiatric illness/social situations that would limit compliance with study requirements. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to lenvatinib, pembrolizumab, or any of the study drug excipients. * Pregnant women are excluded from this study because pembrolizumab and/or lenvatinib are agents with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with pembrolizumab and/or lenvatinib, breastfeeding should be discontinued if the mother is treated with either agent.