A Study to Evaluate Immunotherapy Combinations in Participants With Lung Cancer

Inclusion Criteria: * Male or female participants; age ≥ 18 years * Pathologically confirmed nonsquamous NSCLC that is metastatic, locally advanced, or recurrent with progression * Arm A participants must fulfill one of the following: * Participant has a genetic alteration (mutation or rearrangement) and has received all available targeted therapy. Previous treatment with chemotherapy or PD-1/-L1 therapy is not allowed. * Participant has not received any therapy for the disease under study and standard therapy is refused. * Participant has progressed on PD-1/-L1 therapy (monotherapy or combination regimen). Previous treatment with chemotherapy is not allowed. * Participant has progressed on PD-1/-L1 therapy (monotherapy or combination regimen) and has received less than 4 cycles of carboplatin/pemetrexed and further chemotherapy is appropriate. * Participant has received any number of prior treatments and is without alternative or curative therapy. * Arm B participants must fulfill one of the following: * Participant has a genetic alteration (mutation or rearrangement) and has received all available targeted therapy. Previous treatment with chemotherapy or PD-1/-L1 therapy is not allowed. * Participant has not received any therapy for the disease under study and standard therapy is refused. * Participant has received any number of prior treatments and is without alternative or curative therapy. * Arm 1 and Arm 2 participants must have a sensitizing epidermal growth factor receptor (EGFR) mutation with disease progression or treatment intolerance after one or more approved TKIs. Previous treatment with chemotherapy or PD-1/L-1 therapy is not allowed. * No TKI therapy within 5 days of Cycle 1 Day 1 * The last dose of previous investigational therapy is at least 4 weeks or 5 half-lives prior to Cycle 1 Day 1. * Must have at least 1 measurable lesion per Response Evaluation Criteria in Solid Tumors (RECIST v1.1) * Eastern Cooperative Oncology Group (ECOG) performance status score of 0 or 1. * Confirm that an archival tissue sample is available and ≤ 24 months old; if not, a new biopsy of a tumor lesion should be obtained at screening * Adequate organ and marrow function Exclusion Criteria: * Use of any live vaccines against infectious diseases within 4 weeks (28 days) of initiation of investigational product * Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the pre-screening or screening visit through 30 days after the last dose of etrumadenant, 90 days after the last dose of zimberelimab or pembrolizumab, or 6 months after the last dose of pemetrexed, whichever is longer * Any active autoimmune disease or a documented history of autoimmune disease or syndrome that required systemic treatment in the past 2 years (ie, with use of disease-modifying agents, corticosteroids, or immunosuppressive drugs), except for vitiligo or resolved childhood asthma/atopy * Prior malignancy active within the previous 2 years except for locally curable cancers that have been apparently cured, such as basal or squamous cell skin cancer, superficial bladder cancer, or carcinoma in situ of the cervix, breast, or prostate cancer * Prior use of an adenosine pathway targeting agent * Due to potential for drug-drug interactions with etrumadenant, participants must not have had: * Treatment with breast cancer resistance protein substrates or P-glycoprotein with a narrow therapeutic window, administered orally within 4 weeks or 5 half-lives of the drug (whichever is longer) prior to initiation of study treatment. * Treatment with known strong cytochrome P450 3A4 (CYP3A4) inducers and strong CYP3A4 inhibitors within 4 weeks or 5 half-lives of the drug (whichever is longer) prior to initiation of study treatment