The purpose of this study is to assess the safety and efficacy of pemetrexed + carboplatin + pembrolizumab (MK-3475) with lenvatinib (MK-7902/E7080) in patients with advanced nonsquamous non-small cell lung cancer harboring EGFR mutations.

Inclusion Criteria:

1. Have a histologically or cytologically confirmed diagnosis of incurable Stage IIIB, IIIC, IVA, IVB (American Joint Committee on Cancer [AJCC], version 8) non-squamous NSCLC. Postoperative recurrence is acceptable if the disease is not curable.

2. Have documentation of tumor activating EGFR mutation, specifically either exon 19 deletion or exon 21 L858R.

3. Have investigator determined radiographic disease progression per RECIST 1.1 after treatment with EGFR-TKI therapy:

   1. Participants previously treated with 1st or 2nd generation EGFR TKI (eg, erlotinib/afatinib/gefitinib) are required to have confirmed documented absence of EGFR T790M mutation.
   2. Participants with confirmed acquired T790M mutation after 1st or 2nd generation EGFR-TKI (eg, erlotinib/afatinib/gefitinib) are required to have osimertinib TKI treatment failure prior to enrollment.
   3. Participants previously failed osimertinib TKI treatment as 1st line therapy are eligible regardless of their EGFR T790M mutation status.
   4. Participants treated with a combination of EGFR TKIs and antibodies targeting the VEGF pathway will also be eligible.

4. Have measurable disease per RECIST 1.1.

5. Be male or female ≥ 20 years of age inclusive, at the time of signing the informed consent form (ICF).

6. Have a life expectancy of at least 3 months.

7. Have an ECOG performance status of 0 or 1 within 7 days prior to the first dose of study intervention but before registration.

8. A male participant must agree to use a contraception during the treatment period.

9. A female participant is eligible to participate if she is not pregnant, not breastfeeding

10. The participant provides written informed consent for the study.

11. Have adequate organ function.

12. Have adequately controlled blood pressure (BP) with or without antihypertensive medications, defined as BP ≤ 150/90 mmHg and no change in antihypertensive medications within 1 week prior to registration.

Exclusion Criteria:

1. Has known untreated central nervous system (CNS) metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, clinically stable, and have not required steroids for at least 14 days prior to the first dose of study intervention.

2. Has history of (noninfectious) pneumonitis that required systemic steroids or current pneumonitis/interstitial lung disease.

3. Radiographic evidence of intratumoral cavitations, encasement, or invasion of a major blood vessel. Additionally, the degree of proximity to major blood vessels should be considered because for exclusion because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis after lenvatinib therapy (in the chest, major blood vessels include the main pulmonary artery, the left and right pulmonary arteries, the 4 major pulmonary veins, the superior or inferior vena cava, and the aorta).

4. Has a known history of an additional malignancy, except if the participant has undergone potentially curative therapy with no evidence of that disease of that disease recurrence for at least 3 year since initiation of that therapy.

5. Has an autoimmune disease that has required systemic treatment in the past 2 years (ie, 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 allowed.

6. Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (doses exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior the first dose of study intervention.

7. Has had an allogeneic tissue/solid organ transplant.

8. Has a known history of human immunodeficiency virus (HIV) infection. HIV testing is not required unless mandated by the local health authority.

9. Has a known history of Hepatitis B (defined as Hepatitis B surface antigen [HBsAg] reactive or HBV-DNA detected) or known active Hepatitis C virus (HCV antibody reactive).

10. Has a history of a gastrointestinal condition or procedure that in the opinion of the investigator may affect oral drug absorption.

11. Has active hemoptysis (at least 0.5 tsp of bright red blood) within 2 weeks prior to the first dose of study intervention.

12. Has significant cardiovascular impairment within 12 months prior to the first dose of study intervention, including history of congestive heart failure greater than New York Heart Association (NYHA) Class II, unstable angina, myocardial infarction, cerebrovascular accident (CVA)/stroke, or cardiac arrhythmia associated with hemodynamic instability.

13. Has a known history of active tuberculosis.

14. Has an active infection requiring systemic therapy.

15. 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.

16. Has known psychiatric or substance abuse disorders that would interfere with the participant's cooperation to meet with the requirements of the study.

17. Previously had a severe hypersensitivity reaction to treatment with a monoclonal antibody or has s known sensitivity to any component of lenvatinib or pembrolizumab, or as applicable, carboplatin, or pemetrexed.

18. A women of childbearing potential (WOCBP) who has a positive urine pregnancy test within 72 hours prior to registration. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required.

19. Has preexisting ≥ Grade 3 gastrointestinal or non-gastrointestinal fistula. Prior/Concomitant Therapy

20. Has received prior systemic cytotoxic chemotherapy for their metastatic NSCLC. Note: Prior treatment with chemotherapy and/or radiation as part of neoadjuvant/adjuvant therapy is allowed as long as therapy was completed at least 6 months prior to the diagnosis of metastatic NSCLC.

21. Has received prior treatment with pembrolizumab or any other anti-PD-1, anti-PD-L1, anti-PD-L2 agent, with lenvatinib or any other RTKi, or with an agent directed to another stimulatory or co-inhibitory T cell receptor (eg, CTLA-4, OX-40, CD137, GITR).

22. Has received radiotherapy within 14 days prior to the first dose of study intervention or received lung radiation therapy of > 30 Gy within 6 months prior to the first dose of study intervention.

23. Has received systemic steroid therapy (in doses exceeding 10 mg daily of prednisone equivalent) within 7 days prior to the first dose of study intervention.

24. Has received a live vaccine within 30 days prior to the first dose of study intervention. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, and Bacillus Calmette-Guerin (BCG). Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed.

25. Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks prior to the first dose of study intervention.

    Note: Participants who have entered the follow-up phase of an investigational study may participate as long as it has been > 4 weeks after the last dose of the previous investigational agent.

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

27. Has a prolongation of QTc interval (calculated using Fridericia's formula) of > 480 msec.

28. Has left ventricular ejection fraction (LVFE) below 50% as determined by multigated acquisition scan (MUGA) or echocardiogram (ECHO).

29. 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 ability to participate for the full duration of the study, or make it not in the best interest of the participant to participate, in the opinion of the treating investigator.