This is a phase II study testing the combination of Pembrolizumab with Lenvatinib, a multi-kinase inhibitor that has activity against vascular endothelial growth factor receptors 1-3 (VEGFR1-3), fibroblast growth factor receptors 1-4 (FGFR1-4), ret protooncogene (RET), platelet-derived growth factor receptor-alpha (PDGFR-alpha) and KIT (a stem cell factor receptor), and letrozole, a non-steroidal aromatase inhibitor, in advanced hormone receptor (HR) positive human epidermal growth factor receptor 2 (HER2) negative breast cancer (BC) that has progressed on/after standard endocrine therapy.

Inclusion Criteria:

1. Male/female participants who are at least 21 years of age on the day of signing informed consent, with histologically or cytologically confirmed diagnosis of metastatic or locally advanced carcinoma of the breast not amenable to treatment with curative intent, will be enrolled in this study.

2. Disease progression after treatment with at least 1 line of palliative endocrine therapy in the metastatic setting.

   1. There is no limit to the number of lines of prior palliative endocrine therapy. (Prior aromatase inhibitor in the curative and/or palliative setting is allowed.)

   2. Prior targeted therapy in the locally advanced (recurrent or progressed) or metastatic setting, such as CDK4/6 inhibitors, mTOR inhibitors, PI3K inhibitors, is allowed with no limit to the number of lines of targeted therapy (prior Lenvatinib is not allowed).

   3. Maximum of 1 line of palliative chemotherapy is allowed.

      • A chemotherapy line in advanced disease is an anticancer regimen(s) that contains at least 1 cytotoxic chemotherapy agent and was discontinued due to progression. If a cytotoxic chemotherapy regimen was discontinued for a reason other than disease progression then this regimen does not count as a "prior line of chemotherapy".
      • Antibody-drug conjugate will be considered as cytotoxic chemotherapy in the assessment of the lines of treatment.

3. ER positive and/or PgR positive breast cancer (based on most recent tumor biopsy or archived tumor specimen) according to American Society of Clinical Oncology/College of American Pathologists (ASCO/CAP) guidelines, assessed locally and defined as at least 1% of tumor cells stained positive.

4. HER2-negative tumor assessed locally and defined as meeting one of the following sets of criteria:

   • HER2 IHC score of 0 or 1+
   • HER2 IHC score of 2+ accompanied by a negative fluorescence, chromogenic, or silver in situ hybridization test indicating the absence of HER2 gene amplification
   • HER2/CEP17 ratio of < 2.0 based on the most recent tumor biopsy (or archived tumor sample).

5. For women: postmenopausal or premenopausal/perimenopausal status, defined as follows: Postmenopausal, as defined by at least one of the following criteria:

   • Age ≥ 60 years
   • Age < 60 years and ≥ 12 months of amenorrhea plus follicle-stimulating hormone (FSH) and plasma estradiol levels within postmenopausal range by local laboratory assessment, in the absence of oral contraceptive pills, hormone replacement therapy, or gonadotropin-releasing hormone agonist or antagonist
   • Documented bilateral oophorectomy (≥14 days prior to first treatment on Day 1 of Cycle 1 and recovery from surgery to baseline) Premenopausal or perimenopausal, defined as not meeting the criteria for postmenopausal, and willing to undergo and maintain treatment with approved LHRH-agonist therapy for the duration of study treatment LHRH-agonist therapy may be initiated 14-28 days prior to commencement of letrozole, and continued 4-weekly.

   For men: willing to undergo and maintain treatment with approved LHRH-agonist therapy for the duration of study treatment; LHRH-agonist therapy may be initiated 14-28 days prior to commencement of letrozole, and continued 4-weekly.

6. A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies:

   1. Not a woman of childbearing potential (WOCBP) as defined in protocol OR
   2. A WOCBP who agrees to follow the contraceptive guidance in protocol during the treatment period and for at least 120 days (corresponding to time needed to eliminate pembrolizumab and/or any active comparator/combination) plus 30 days (a menstruation cycle) after the last dose of study treatment.

7. A male participant must agree to use a contraception during the treatment period and for at least 120 days, corresponding to time needed to eliminate pembrolizumab plus an additional 90 days (a spermatogenesis cycle) after the last dose of study treatment and refrain from donating sperm during this period.

8. The participant provides written informed consent for the trial.

9. 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.

10. Availability of tumor sample:

    • Patient should have a site of disease amenable to biopsy, and be a candidate for tumor biopsy according to the treating institutions guidelines. Patient must be willing to undergo a new tumor biopsy at screening. Bone metastases are not acceptable.
    • A representative tumor sample obtained after progression on the patients most recent endocrine therapy must be submitted
    • In the event that a post-progression sample is not available and a new biopsy cannot be obtained, enrolment may be considered after documented discussion with the Principal Investigator and the study team for a waiver.

11. 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.

12. Life expectancy of more than 12 weeks.

13. Adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP ≤150/90 mmHg at screening and no change in antihypertensive medications within 1 week prior to the Cycle 1 Day -14.

14. Have adequate organ and haematological functions as defined in the protocol.

Exclusion Criteria:

1. A WOCBP who has a positive urine pregnancy test within 72 hours prior to allocation. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required.

   Note: in the event that 72 hours have elapsed between the screening pregnancy test and the first dose of study treatment, another pregnancy test (urine or serum) must be performed and must be negative in order for subject to start receiving study medication.

2. 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).

3. Has received prior Lenvatinib.

4. Has received prior systemic anti-cancer therapy including investigational agents within 4 weeks (or 5 times the half-life, whichever is shorter) prior to allocation. 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. Participants with endocrine-related AEs Grade ≤2 requiring treatment or hormone replacement may be eligible.

5. Lack of adequate recovery from any toxicity and/or complications from any toxicity and/or complications from major surgery prior to starting therapy.

6. 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-CNS disease.

7. Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of study drug. Administration of killed vaccines is allowed.

8. Is currently participating in or has participated in a study of an investigational agent or has used an investigational device within 4 weeks (or 5 times the half-life for systemic agent(s), whichever is shorter) prior to the first dose of study intervention.

9. 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.

10. Has a known additional malignancy that is progressing or has required active treatment within the past 3 years. Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin or carcinoma in situ (eg, breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded.

11. 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 intervention.

12. Has severe hypersensitivity (≥Grade 3) to Pembrolizumab, Lenvatinib, Letrozole and/or any of its excipients.

13. 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 (eg thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment and is allowed. Subjects with T3, free T3 or free T4 abnormalities at screening who are asymptomatic can be eligible, but will need to be monitored closely with correction of abnormalities as clinically indicated.

14. Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease.

15. Subjects having >1+ proteinuria on urinalysis will undergo 24-hour urine collection for quantitative assessment of proteinuria. Subjects with urine protein ≥1 g/24-hour will be ineligible.

16. Gastrointestinal malabsorption, gastrointestinal anastomosis, or any other condition that might affect the absorption of Lenvatinib.

17. New York Heart Association congestive heart failure of grade II or above, unstable angina, myocardial infarction within the past 6 months, or serious cardiac arrhythmia associated with significant cardiovascular impairment within the past 6 months.

18. Prolongation of QTc interval to >480 msec.

19. Active hemoptysis (bright red blood of at least 0.5 teaspoon) within 3 weeks prior to the first dose of study drug.

20. Serious nonhealing wound, ulcer, or bone fracture

21. Has an active infection requiring systemic therapy. Hepatitis B and/or C infection may be allowed if controlled (see criterion 23 below).

22. Has a known history of Human Immunodeficiency Virus (HIV) infection. Note: No HIV testing is required unless mandated by local health authority.

23. Has a known history of Hepatitis B (defined as Hepatitis B surface antigen [HBsAg] reactive) or known active Hepatitis C virus (defined as HCV RNA [qualitative] is detected) infection. Note: no testing for Hepatitis B and Hepatitis C is required unless mandated by local health authority. The presence of hepatitis B core antibody (HBcAb) will not be an exclusion criterion provided HBsAg is negative and Hepatitis B virus DNA is not detected.

24. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the participant's participation for the full duration of the study, or is not in the best interest of the participant to participate, in the opinion of the treating investigator.

25. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.

26. Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of trial treatment.

27. Has had an allogenic tissue/solid organ transplant.