Inclusion Criteria:  Have a histologically or cytologically confirmed stage IV NSCLC by American Joint Committee on Cancer Version 8 Have confirmation with sensitizing EGFR mutations, either DEL19 or L858R Have undergone failure 1-2 prior EGFR-TKI (Osimertinib exposure required for T790M+)  Have measurable disease based on RECIST 1.1, as determined by the local site.  - Note: Lesions that appear measurable but are situated in a previously irradiated area can be considered measurable (eligible for selection as target lesions) if they have shown documented growth since the completion of radiation.  Tumor tissue that demonstrates PD-L1 expression in ≥1% of tumor cells (TPS ≥1%) as assessed by IHC 22C3 pharmDx.  Note: Assessment of PD-L1 expression must be made from provided archival tumor tissue sample or newly obtained core or excisional biopsy of a tumor lesion not previously irradiated. (A fine-needle aspirate, frozen sample, plastic embedded sample, cell block, clot, bone, bone marrow, cytologic specimen, or decalcified or formalin-fixed sample that was frozen at any point will not be acceptable for analysis). Formalin-fixed, paraffin-embedded tissue blocks are preferred to slides. Newly obtained biopsies are preferred to archived tissue.  Exclusion Criteria:  Has known untreated central nervous system metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable (ie, without evidence of progression for at least 4 weeks by repeat imaging (note: repeat imaging should be performed during study screening), clinically stable, and without requirement of steroid treatment for at least 14 days before first dose of study intervention. Has clinically significant hemoptysis (at least 0.5 teaspoon of bright red blood) or tumor bleeding within 2 weeks before the first dose of study intervention. Bleeding or thrombotic disorders or subjects at risk for severe hemorrhage. The degree of tumor invasion/infiltration of major blood vessels should be considered because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis after lenvatinib therapy.  Has a known history of an additional malignancy, except if the participant has undergone potentially curative therapy with no evidence of that disease recurrence for at least 3 years since initiation of that therapy.  - Note: The time requirement for no evidence of disease for at least 3 years does not apply to the NSCLC for which a participant is enrolled in the study. The time requirement also does not apply to participants who underwent successful definitive resection of basal cell carcinoma of the skin, superficial bladder cancer, squamous cell carcinoma of the skin, in situ cervical cancer, or other in situ cancers.  Has an active autoimmune disease that has required systemic treatment in the past 2 years (ie, with the 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. Has had an allogeneic tissue/solid organ transplant. Has a known history of human immunodeficiency virus (HIV) infection; HIV testing is not required unless mandated by the local health authority. Has a history of (noninfectious) pneumonitis that required systemic steroids or current pneumonitis/interstitial lung disease.  Has a known history of hepatitis B (defined as hepatitis B surface antigen [HBsAg] reactive or hepatitis B virus [HBV]-DNA detected) or known active hepatitis C virus (HCV, defined as HCV-RNA [qualitative] detected or HCV antibody reactive, if HCV-RNA is not the local SOC) infection.  - Note: No testing for hepatitis B and hepatitis C is required unless mandated by the local health authority.  Has a history of a gastrointestinal condition or procedure that in the opinion of the investigator may affect oral study drug absorption. Has significant cardiovascular impairment within 12 months of the first dose of study intervention, such as a history of congestive heart failure greater than New York Heart Association Class II, unstable angina, myocardial infarction, cerebrovascular accident (CVA)/stroke, or cardiac arrhythmia associated with hemodynamic instability. Has not recovered adequately from any toxicity and/or complications from major surgery before starting therapy. Has a known history of active tuberculosis (TB). Has an active infection requiring systemic therapy. Has a known psychiatric or substance abuse disorder that would interfere with the participant's cooperation for the requirements of the study. Previously had a severe hypersensitivity reaction to treatment with an mAb or has a known sensitivity or intolerance to any component of lenvatinib or pembrolizumab.  WOCBP who has a positive urine pregnancy test 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.  - Note: In the event that 72 hours have elapsed between the screening pregnancy test and the first dose of study intervention, another pregnancy test (urine or serum) must be performed and must be negative for the participant to start receiving study intervention.  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 study intervention. Has received a live vaccine within 30 days prior to the first dose of study drug. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (eg, FluMist®) are live attenuated vaccines and are not allowed.