Study of Lenvatinib w/ Pembro in Black Participants w/Mismatch Repair-Prof Recurrent Endometrial Cancer

Inclusion Criteria: * Histologically and/or cytologically confirmed endometrioid, serous, clear cell, carcinosarcoma, or de-differentiated or undifferentiated endometrial cancer with radiographic and/or clinical evidence of disease progression * Documented microsatellite stable disease as tested by either microsatellite instability polymerase chain reaction (MSI PCR) or deoxyribonucleic acid (DNA) mismatch repair (MMR) by immunohistochemistry (IHC) * Self-identify as being of predominantly (\>50%) Black race, inclusive of Black, African-American, Black Hispanic (Afro-Latinx), African, or Afro-Caribbean ancestry * Received, ineligible for (by investigator determination), or declined platinum containing chemotherapy * Received no greater than two prior lines of therapy. Maintenance therapies and hormonal therapies will NOT count as a line of therapy. * Measurable disease as determined by RECIST v1.1: * At least one lesion of ≥10 mm in the longest diameter for a non-lymph node, or ≥15 mm in the short-axis diameter for a lymph node that is serially measurable using computerized tomography/magnetic resonance imaging (CT/MRI) * Target lesions limited to a radiated field must show evidence of substantial size increase according to previous scans to be deemed a target lesion * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 * Ability to swallow oral medications * Patients who are not postmenopausal or have not undergone hysterectomy must have a documented negative serum pregnancy test within 72 hours prior to initiating study treatment Note: Postmenopausal is defined as any of the following: * Age ≥ 60 years * Age \< 60 years and amenorrheic for at least 1 year with follicle-stimulating hormone (FSH) and plasma estradiol levels in the postmenopausal range * Bilateral oophorectomy * Patients of child-bearing potential must agree to use a medically accepted method for preventing pregnancy during and for a minimum of 4 months following the last dose of lenvatinib or pembrolizumab * Patients with known brain metastases will be eligible if they have completed primary brain therapy (such as whole brain radiotherapy, stereotactic radiosurgery, or complete surgical resection) and if they have remained clinically stable, asymptomatic, and off of steroids for at least 28 days before starting study treatment * Toxicities from previous cancer therapies resolved to grade ≤1 unless specified otherwise (exceptions: chronic residual toxicities that in the opinion of the investigator are not clinically relevant, given the known safety/toxicity profiles of Lenvatinib and pembrolizumab, such as alopecia, grade ≤2 anemia; neuropathy related to previous chemotherapy must be resolved to grade ≤2) * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Carcinosarcoma (malignant mixed mullerian tumor), endometrial leiomyosarcoma, or endometrial stromal sarcoma * Unstable central nervous system (CNS) metastases * Gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of lenvatinib * Pre-existing grade ≥3 gastrointestinal or non-gastrointestinal fistula * Radiographic evidence of major blood vessel invasion/infiltration * Clinically significant hemoptysis or tumor bleeding within 2 weeks prior to the first dose of study treatment * History of congestive heart failure greater than New York Heart Association (NYHA) Class II, unstable angina, myocardial infarction, cerebrovascular accident, stroke, or cardiac arrhythmia associated with hemodynamic instability within 12 months of the first dose of study treatment * Known history or evidence of interstitial lung disease or active, non-infectious pneumonitis * Administration of or condition requiring administration of systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to initiating study treatment Exception: Patients with conditions that can be managed with steroids equivalent to or less than an oral prednisone dose of 10 mg daily are not excluded from the study * Active autoimmune disease (with the exception of psoriasis) that has required systemic treatment in the past 2 years (ie, with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs) or a documented history of clinically severe autoimmune disease or a syndrome that requires systemic steroids or immunosuppressive agents Note: Patients with the conditions or medical history listed below are not excluded from the study. * Vitiligo * Resolved childhood asthma/atopy * Requirement for intermittent use of bronchodilators or local steroid injections or topical steroids * Hypothyroidism stable on hormone replacement * Sjogren's Syndrome * Has received \>1 prior systemic chemotherapy regimen (other than adjuvant or neoadjuvant) for endometrial cancer; participants may receive up to two regimens of platinum-based chemotherapy in total, as long as one is given in the neoadjuvant or adjuvant treatment setting * Prior anticancer treatment within 28 days of study start * Prior treatment with any treatment targeting Vascular endothelial growth factor (VEGF)-directed angiogenesis, any anti-PD-1, anti-PD-L1, or anti-PD-L2 agent * Has received prior treatment with an agent directed to a stimulatory or co-inhibitory T-cell receptor other than an anti-PD-1, anti-PD-L1, or anti-PD-L2 agent, and who has discontinued from that treatment due to a grade 3 or higher immune-related adverse event (irAE) * Has received prior radiation therapy within 21 days of study start with the exception of palliative radiotherapy to bone lesions, which is allowed if completed 2 weeks of study start; participants must have recovered from all radiation-related toxicities and/or complications prior to randomization * Participants with urine protein ≥3.5 gram (g)/24 hour * Left ventricular ejection fraction (LVEF) below the institutional normal range as determined by multigated acquisition scan (MUGA) or echocardiogram (ECHO) * Prior immunotherapy (single or dual immune checkpoint inhibition, cellular or vaccine therapy) * Administration of a live vaccine within 30 days prior to initiating study treatment Note: Seasonal influenza vaccines for injection are generally inactivated flu vaccines and are permitted; however, intranasal influenza vaccines (e.g., Flu-Mist) are live attenuated vaccines, and are not allowed. Coronavirus Disease 2019 (COVID-19) vaccines are allowed and encouraged * Administration of any investigational agent within 4 weeks prior to initiating study treatment * History of solid organ or allogeneic stem cell transplant * Known intolerance to either of the study drugs (or any of the excipients) * Known immunodeficiency, eg, human immunodeficiency virus (HIV) Note: HIV testing is not required for eligibility screening * Known active hepatitis B or C Note: hepatitis B and C testing is not required for eligibility screening * Serious (ie, grade ≥3) uncontrolled infection * Pregnancy or breastfeeding * Diagnosis or treatment for another malignancy within 2 years prior to study registration, with the following exceptions: complete resection of basal cell carcinoma or squamous cell carcinoma of the skin, any in situ malignancy * Medical, psychological, or social condition that, in the opinion of the investigator, may increase the patient's risk or limit the patient's adherence with study requirements