Study of LY3537982 in Cancer Patients With a Specific Genetic Mutation (KRAS G12C)

Inclusion Criteria: * Patients have measurable disease per Response Evaluation Criteria in Solid Tumors version 1.1 (RECIST v1.1). * Patients must have disease with evidence of KRAS G12C mutation in tumor tissue or circulating tumor deoxyribonucleic acid (DNA). * Participants must have a histological or a cytologically proven diagnosis of locally advanced, unresectable, and/or metastatic cancer and meet cohort-specific criteria. * Have an Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1. * Have adequate organ function. * Have discontinued all previous treatments for cancer with resolution of any significant ongoing adverse events (AEs), (except in certain scenarios). * Must be able to swallow capsule/tablet. * Agree and adhere to contraceptive use, if applicable. * For some parts of the study, (i.e., one of the two arms with LY3537982 in combination with pembrolizumab and the arm of LY3537982 in combination with pembrolizumab, pemetrexed, and platinum therapy) histologically or cytologically confirmed Stage IIIB-IIIC or Stage IV NSCLC that is previously untreated in the advanced/metastatic setting and not suitable for curative intent radical surgery or radiation therapy. Previously untreated patients who received adjuvant and neoadjuvant therapy are eligible if the last dose of the systemic treatment was completed at least 6 months prior to enrollment. For untreated patients in the arm with LY3537982 in combination with pembrolizumab noted above, a single cycle of pembrolizumab may be initiated within 21 days prior to enrollment. For untreated patients in the arm of LY3537982 in combination with pembrolizumab, pemetrexed, and platinum therapy, a single cycle of any or all of the drugs other than LY3537982 may be initiated within 21 days prior to enrollment. Start of study treatment may be delayed to allow sufficient time for recovery from treatment-related toxicity. * For one part of the study, participants must have received at least one prior oxaliplatin- or irinotecan-containing regimen for advanced or metastatic CRC. Exclusion Criteria: * Disease suitable for local therapy administered with curative intent. * Have an active, ongoing, or untreated infection. * Have a serious pre-existing medical condition(s) that, in the judgment of the investigator, would preclude participation in this study. * Have a serious cardiac condition. * Have a second active primary malignancy or have been diagnosed and/or treated for an additional malignancy within 3 years prior to enrollment. * For some parts of the study only: have untreated active central nervous system (CNS) metastases and/or leptomeningeal disease. Patients with treated CNS metastases are eligible for this study if their disease is asymptomatic, radiographically stable for at least 30 days, and they do not require treatment with steroids in the two-week period prior to study treatment. Patients with active CNS metastases are eligible for one part of the study. * Have received prior treatment with any KRAS G12C small molecule inhibitor, except in certain scenarios where such prior therapy is allowed as per protocol. * The following patients will be excluded from some parts of the study: * Experienced certain serious side effects with prior immunotherapy. * Have an active autoimmune disease that has required systemic anti-autoimmune treatment in the past 2 years. * Have received a live vaccine within 30 days prior to the first dose of study drug. * Pregnant, breastfeeding, or expecting to conceive or father children within the projected duration of the trial through 35 days after the last dose of study medication. * Known allergic reaction against any of the components of the study treatments.