A Study of Lenvatinib, Pembrolizumab, and Fulvestrant in People With Breast Cancer

Inclusion Criteria: * Male or female participants who are ≥18 years old with histologically confirmed diagnosis of unresectable locally advanced or MBC. * Male participants or premenopausal females are eligible as long as they are on LHRH agonist for at least four weeks prior to starting trial therapy and commit to continue LHRH agonist for as long as patient is receiving trial therapy or medical contraindications arise * Patients diagnosed with ER+ (ER \>1%), HER2- breast cancer as per American Society of Clinical Oncology (ASCO)/College of American Pathologists (CAP) guidelines. * Progressed on at least 1 prior endocrine therapy combined with CDK 4/6 inhibitor. Prior fulvestrant therapy is permitted. * Have not received more than 2 lines of chemotherapy in the metastatic setting. * Stable previously treated brain metastases i.e. without radiological evidence of progression for at least 4 weeks (note that repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at * Life expectancy of ≥12 weeks. * A newly obtained biopsy of non-irradiated tumor must be available prior to the first dose of study drug for biomarker analysis. Patients with inaccessible tumors for biopsy specimens can be enrolled without a biopsy (if archival tissue is available within the previous 6-12 months) upon consultation and agreement by the Principal Investigator. Formalin-fixed, paraffin embedded (FFPE) tissue blocks are favored over slides and fresh tissue biopsies are preferred over archival tissue * The participant provides written informed consent for the trial. * Have measurable disease based on RECIST 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions. * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1. Evaluation of ECOG is to be performed within 7 days prior to the first dose of study intervention. * Have adequately controlled BP with or without antihypertensive medications, defined as BP ≤150/90 mm Hg with no change in antihypertensive medications within 1 week prior to randomization. * Have adequate organ function. Specimens must be collected within 14 days prior to the start of study intervention. * 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 woman of childbearing potential (WOCBP) OR * Is a WOCBP and using a contraceptive method that is highly effective (with a failure rate of \<1% per year), with low user dependency, or be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis), during the intervention period and for at least 120 days post pembrolizumab or 30 days post lenvatinib, whichever occurs last. The investigator should evaluate the potential for contraceptive method failure (i.e.,noncompliance, recently initiated) in relationship to the first dose of study intervention * A WOCBP must have a negative urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of beta-human chorionic gonadotropin \[β-hCG\]) within 72 hours before the first dose of study intervention. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required. * Additional requirements for pregnancy testing during and after study intervention. * The investigator is responsible for review of medical history, menstrual history, and recent sexual activity to decrease the risk for inclusion of a woman with an early undetected pregnancy. * Male participants are eligible to participate if they agree to the following during the intervention period and for at least 7 days after the last dose of lenvatinib: * 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 (vasectomized or secondary to medical cause) as detailed below: * Agree to use a male condom plus partner use of an additional contraceptive method when having penile-vaginal intercourse with a WOCBP who is not currently pregnant. Note: Men with a pregnant or breastfeeding partner must agree to remain abstinent from penile-vaginal intercourse or use a male condom during each episode of penilevaginal penetration. Please note that 7 days after lenvatinib is stopped, if the participant is on pembrolizumab only, no male contraception measures are needed. Criteria for known Hepatitis B and C positive subjects: * Hepatitis B and C screening tests are required as per MSK policy but do not need to be repeated prior to study unless there is a known history of Hepatitis B Virus (HBV) or Hepatitis C Virus (HCV) infection. * Participants who have active hepatitis B infection (defined as HBsAg positive and/or detectable HBV DNA) are eligible if they have received HBV antiviral therapy for at least 4 weeks and have undetectable HBV viral load prior to randomization. Participants should remain on anti-viral therapy throughout study intervention and follow MSK guidelines for HBV anti-viral therapy post completion of study intervention. * Participants with a history of HCV infection (defined as anti-HCV Ab positive and detectable HCV RNA) are eligible if HCV viral load is undetectable at screening. Participants must have completed curative anti-viral therapy at least 4 weeks prior to randomization. ° Adequate Organ Function Laboratory Values * Hematological Absolute neutrophil count (ANC) ≥1500/µL * Platelets ≥100 000/µL * Hemoglobin ≥9.0 g/dL or ≥5.6 mmol/La °Renal * Creatinine OR Measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCl) ≤1.5 × ULN OR ≥30 mL/min for participant with creatinine levels \>1.5 × ULN °Hepatic * Total bilirubin ≤1.5 × ULN OR direct bilirubin ≤ULN for participants with total bilirubin levels \>1.5 × ULN * AST (SGOT) and ALT (SGPT) ≤2.5 × ULN (≤5 × ULN for participants with liver metastases) °Coagulation * International normalized ratio (INR) OR prothrombin time (PT) Activated partial thromboplastin time (aPTT) ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants ALT (SGPT)=alanine aminotransferase (serum glutamic pyruvic transaminase); AST (SGOT)=aspartate aminotransferase (serum glutamic oxaloacetic transaminase); GFR=glomerular filtration rate; ULN=upper limit of normal. a Criteria must be met without erythropoietin dependency and without packed red blood cell (pRBC) transfusion within last 2 weeks. b Creatinine clearance (CrCl) should be calculated per institutional standard. Note: This table includes eligibility-defining laboratory value requirements for treatment; laboratory value requirements should be adapted according to local regulations and guidelines for the administration of specific chemotherapies. 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). * Prior exposure to lenvatinib or any other VEGF-directed anti-angiogenic agent. * Has received prior systemic anti-cancer therapy including investigational agents within 2 weeks prior to allocation. All acute toxicities related to prior systemic treatments must be resolved to Grade ≤1, except for alopecia and Grade ≤2 peripheral neuropathy. * Has received prior radiotherapy within 2 weeks of start of study intervention. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-central nervous system (CNS) disease. * Has received a live vaccine or live-attenuated vaccine within 30 days before the first dose of study intervention. Administration of non-live-attenuated vaccines is permitted. Note: please refer to Section 10.5 for information on COVID-19 vaccines * Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 2 weeks prior to the first dose of study intervention. * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in doses \>10 mg daily of oral prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug. Inhaled, intranasal, intra-articular, or topical steroid use are allowed. * Has a known additional malignancy that is progressing or has required active treatment within the past 3 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin or carcinoma in situ, excluding carcinoma in situ of the bladder, 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 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 intervention. * Has a history or evidence of active pneumonitis or interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. * Has an active infection requiring antibiotics. * Has a known history of Human Immunodeficiency Virus (HIV) infection. * Has an inability to swallow capsules. * Has a history or current evidence of any condition, therapy, or laboratory abnormality or other circumstance that might confound the results of the study, interfere with the participant's participation for the full duration of the study, such that it is not in the best interest of the participant to participate, in the opinion of the treating investigator. * Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. * Is pregnant or breastfeeding or expecting to conceive within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment. * Has had an allogenic tissue/solid organ transplant. * Has gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of lenvatinib. * Has clinically significant hemoptysis (≥0.5 teaspoon of bright red blood) or tumor bleeding within 2 weeks prior to the first dose of study drug. * Has significant cardiovascular impairment within 12 months of the first dose of study drug: such as NYHA Class III or IV congestive heart failure, unstable angina, myocardial infarction, cerebral vascular accident, or cardiac arrhythmia associated with hemodynamic instability. Note: Medically controlled arrhythmia would be permitted. * Has a left ventricular ejection fraction (LVEF) below the institutional normal range of 50%, as determined by multigated acquisition (MUGA) or echocardiogram (ECHO). * Prolongation of QTcF interval to \>480 ms. Note: If the QTcF is prolonged to \>480 ms in the presence of a pacemaker, contact the sponsor to determine eligibility. * Has significant vascular disease: such as an aortic aneurysm requiring surgical repair or peripheral arterial thrombosis. Note: history of deep venous thrombosis (DVT) is permitted. * Has active autoimmune disease (with the exception of psoriasis) 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) is not considered a form of systemic treatment. * Known intolerance to any of the study drugs (or any of the excipients). * Has had major surgery within 3 weeks prior to first dose of study interventions. Note: Adequate wound healing after major surgery must be assessed clinically, independent of time elapsed for eligibility. * Has preexisting ≥Grade 3 gastrointestinal or non-gastrointestinal fistula. * Has urine protein ≥1 g/24 hours. Urine dipstick is the preferred method for testing urinary protein, however, urinalysis may be used if the use of urine dipsticks is not feasible. Note: Participants with proteinuria ≥2+ (≥100 mg/dL) on urine dipstick testing (urinalysis) will undergo 24-hour urine collection for quantitative assessment of proteinuria. * Has radiographic evidence of encasement or invasion of a major blood vessel, or of intratumoral cavitation. Note: The degree of proximity to major blood vessels should be considered because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis following lenvatinib therapy.