Phase II Study of Pembrolizumab in Combination With Lenvatinib in Patients With TNBC, NSCLC, and Other Tumor Types and Brain Metastases

Inclusion Criteria: Patients are eligible to be included in the study only if all the following criteria apply: 1. Male/female patients who are at least 18 years of age on the day of signing informed consent with histologically or cytologically confirmed TNBC (Cohort 1), NSCLC (Cohort 2), or solid tumors other than TNBC and NSCLC (Cohort 3) with brain metastasis and with or without active extracranial disease will be enrolled in this study. 2. Has at least 1 measurable brain metastasis: Presence of at least 1 independently verified measurable brain metastasis in accordance with mRECIST (Appendix 1) that can be accurately assessed at baseline and suitable for accurate repeated measurements and with a tumor diameter of 0.5-3 cm on magnetic resonance imaging \[MRI\]). * Previous SRS and excision of up to 5 brain metastases are permitted at least 3 weeks prior to study treatment initiation, provided that neurologic sequelae have completely resolved and measurable untreated lesion(s) remain. If the patient had prior whole brain radiation therapy or SRS, progression in any measurable brain metastasis must have occurred at least 1 month after the end of radiation therapy for the irradiated lesion to be counted as measurable. * Patients can have asymptomatic (no neurologic signs or symptoms, not requiring immediate local intervention \[surgery or radiosurgery\] or systemic glucocorticoid therapy \[within 10 days prior to study treatment initiation\]) OR minimally symptomatic brain metastases (requiring ≤10 mg prednisone or equivalent per day and not requiring immediate surgical or radiation therapy in the opinion of the treating investigator and a radiation therapy or neurosurgical consultant). 3. Extracranial disease is not required and if present, it can be measurable or non-measurable (RECIST v1.1). 4. A female patient 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 Appendix 6 OR 2. A WOCBP who agrees to follow the contraceptive guidance in Appendix 6 during the treatment period and for at least 120 days after the last dose of study treatment. 5. A male patient must agree to use contraception as detailed in Appendix 6 of this protocol during the treatment period and for at least 120 days after the last dose of study treatment and refrain from donating sperm during this period. 6. The patient (or legally acceptable representative if applicable) provides written informed consent for the study. 7. Has Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 (Appendix 7). 8. Has a life expectancy ≥12 weeks. 9. Has adequate organ function within 28 days of study treatment initiation as defined below: * Absolute neutrophil count ≥1000/µL (without granulocyte colony-stimulating factor support within 2 weeks of laboratory test used to determine eligibility) * Platelet count ≥100 000/µL (without transfusion within 2 weeks of laboratory test used to determine eligibility) * Hemoglobin ≥9.0 g/dL * Total bilirubin ≤1.5 × upper limit of normal (ULN); if hepatic metastases are present, ≤2.0 × ULN * Aspartate transaminase (AST) and alanine transaminase (ALT) ≤2.5 × ULN; if hepatic metastases are present, ≤5.0 × ULN * Creatinine clearance ≥50 mL/min * International normalized ratio (INR) OR prothrombin time (PT) and activated partial thromboplastin time (aPTT) ≤1.5 × ULN. 10. Adequately controlled blood pressure with 0 or 1 antihypertensive medication (defined as blood pressure ≤150/90 mmHg at screening and no changes in antihypertensive medication within 7 days of Day 1 of Cycle 1). 11. Hepatitis B and C screening tests are not required unless: * Known history of HBV or HCV infection * As mandated by local health authority 11.1 Hepatitis B positive subjects * Participants who are HBsAg positive 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 local guidelines for HBV anti-viral therapy post completion of study intervention 11.2 Participants with history of HCV infection 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. Exclusion Criteria: Patients are excluded from the study if any of the following criteria apply, unless medically indicated and after approval by study chair/IRB office: 1. Has NSCLC with an oncogenic driver mutation (mutation\[s\] in EGFR, ERBB2, or BRAF V600E; fusion/rearrangement\[s\] in ALK, ROS1, NTRK, or RET; or MET amplification). KRAS or PIK3CA mutation are allowed. 2. Has hepatocellular carcinoma. NOTE: patients with hepatocellular carcinoma and brain metastasis are excluded from this trial because the dose of lenvatinib approved for this disease is different than the ones used in this trial. 3. Has symptomatic or untreated spinal cord compression. Patients with clinical or radiographic evidence of leptomeningeal metastases or other metastatic systemic disease are not allowed. In cases where brain metastases are superficially located (cortical-based brain metastasis) and leptomeningeal spread is suspected, a work-up for leptomeningeal disease (LMD) should be performed (MRI and lumbar puncture with CSF cytology). If LMD is not confirmed, the treating physician, neuro-oncologist, or brain metastasis multidisciplinary team should make a clinical call and exclude the patient if LMD dissemination is likely. 4. Has received prior therapy with lenvatinib or other antiangiogenic tyrosine kinase inhibitor alone or in combination with a PD-1/PD-L1 inhibitor. Prior therapy with an anti-PD-1, anti-PD-L1, anti-PD L2, or anti-CTLA-4 agent or chemotherapy is allowed. 5. Has received prior systemic