Part 2 Cohorts A and C This study is being conducted to test the safety and pharmacokinetics of cemiplimab in patients with lung cancer. The study is also being conducted to test if cemiplimab, alone or in combination, can reduce the size of your tumor by helping the immune system destroy the tumor.

Part 2 Cohorts D and E This study is being conducted to test the safety and pharmacokinetics of fianlimab and cemiplimab in patients with lung cancer. The study is also being conducted to test if fianlimab and cemiplimab, with or without chemotherapy, can reduce the size of your tumor by helping the immune system destroy the tumor.

Key Inclusion Criteria:

1. Disease types under study:

   • Part 1: Histologically or cytologically confirmed diagnosis of malignancy with no alternative standard-of-care therapeutic option
   • Part 2: Patients with histologically or cytologically documented squamous or non-squamous NSCLC with stage IIIB or IIIC or stage IV disease who received no prior systemic treatment for recurrent or metastatic NSCLC.
   • Patients in Part 2 NSCLC cohorts must have available archival or newly obtained formalin-fixed tumor tissue from a metastatic/recurrent site, which has not previously been irradiated.

2. ECOG (Eastern Cooperative Oncology Group) PS (Performance status) ≤1 (Restricted in physically strenuous activity but ambulatory and able to carry out work of a light or sedentary nature [eg, light housework or office work]). Note: Patients with ECOG PS >1 are ineligible.

3. Patients must have been born in Japan, and their biological parents and grandparents must all have been of Japanese origin

4. Willing and able to comply with clinic visits and study-related procedures

5. For Part 2, Cohorts D and E: Available tissue for retrospective testing using assay performed by a central laboratory, as specified in the study manual.

Key Exclusion Criteria:

1. Ongoing or recent (within 5 years) evidence of significant autoimmune disease that requires treatment with systemic immunosuppressive treatments, which may suggest risk for Immune-mediated adverse event (imAE)s. The following are not exclusionary: vitiligo, childhood asthma that has resolved, residual hypothyroidism that requires only hormone replacement or psoriasis that does not require systemic treatment.
2. Untreated brain metastasis (es) that may be considered active. Patients with previously treated brain metastases may participate provided they are stable, there is no evidence of new or enlarging brain metastases, and the patient does not require any systemic corticosteroids for management of brain metastases within 4 weeks prior to the first dose of cemiplimab.
3. Immunosuppressive corticosteroid doses (>10 mg prednisone daily or equivalent) within 4 weeks prior to the first dose of cemiplimab.
4. Any positive test (ribonucleic acid (RNA) or Deoxyribonucleic acid (DNA) by polymerase chain reaction) for hepatitis B, hepatitis C, or human immunodeficiency virus indicating uncontrolled active or chronic infection.
5. History of pneumonitis or interstitial lung disease
6. Surgery within 1 month of first dose and radiation therapy within 2 weeks of first dose
7. Completed palliative radiation therapy within the prior 2 weeks or has not recovered from any medically significant radiation-related Adverse Event (AE)
8. Patients that have never smoked, defined as smoking ≤100 cigarettes in a lifetime (Part 2)
9. Patients with tumors tested positive for epidermal growth factor receptor (EGFR) gene mutations, anaplastic lymphoma kinase (ALK) gene translocations, or ROS1 fusions (Part 2)

Note: Other protocol defined inclusion/exclusion criteria apply.