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)