Testing the Use of Targeted Treatment (AMG 510) for KRAS G12C Mutated Advanced Non-squamous Non-small Cell Lung Cancer (A Lung-MAP Treatment Trial)

Inclusion Criteria: * Participants must be assigned to S1900E. Assignment to S1900E is determined by the LUNGMAP protocol genomic profiling using the FoundationOne assay. Biomarker eligibility for S1900E is based on the identification of a KRAS\^G12C mutation * Participants must have confirmed stage IV or recurrent non-squamous non-small cell lung cancer (NSCLC). Mixed histology NSCLC with less than 50% squamous component is allowed * Participants must have measurable disease documented by computed tomography (CT) or magnetic resonance imaging (MRI). The CT from a combined positron emission tomography (PET)/CT may be used to document only non-measurable disease unless it is of diagnostic quality. Measurable disease must be assessed within 28 days prior to sub-study registration. Pleural effusions, ascites and laboratory parameters are not acceptable as the only evidence of disease. Non-measurable disease must be assessed within 42 days prior to sub-study registration. Participants whose only measurable disease is within a previous radiation therapy port must demonstrate clearly progressive disease (in the opinion of the treating investigator) prior to registration * Participants must have a CT or MRI scan of the brain to evaluate for central nervous system (CNS) disease within 42 days prior to sub-study registration * Participants with known human immunodeficiency virus (HIV) infection must be receiving anti-retroviral therapy and have an undetectable viral load at their most recent viral load test within 6 months prior to sub-study registration * Participants with EGFR sensitizing mutations, EGFR T790M mutation, ALK gene fusion, ROS1 gene rearrangement, or BRAF V600E mutation must have progressed following all standard of care targeted therapy * Participants with spinal cord compression or brain metastases must have received local treatment to these metastases and remained clinically controlled and asymptomatic for at least 7 days following stereotactic radiation and/or 14 days following whole brain radiation, and prior to sub-study registration * Participants must have received at least one line of systemic treatment for stage IV or recurrent NSCLC * Participants must have progressed (in the opinion of the treating physician) following the most recent line of systemic therapy for NSCLC * Participants must have recovered (=\< grade 1) from side effects of prior therapy. The exception is if a side effect from a prior treatment is known to be permanent without expected further recovery or resolution (i.e., endocrinopathy from immunotherapy or cisplatin neurotoxicity) * Participants must be able to swallow tablets whole * Pre-study history and physical exam must be obtained within 28 days prior to sub-study registration * Absolute neutrophil count (ANC) \>= 1,500/uL obtained within 28 days prior to sub-study registration * Platelet count \>= 75,000/uL obtained within 28 days prior to sub-study registration * Hemoglobin \>= 9 g/dL obtained within 28 days prior to sub-study registration * Serum bilirubin =\< institutional upper limit of normal (IULN) within 28 days prior to sub-study registration * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 2 x IULN within 28 days prior to sub-study registration. For participants with liver metastases, and ALT and AST must be =\< 5 x IULN * Participants must have a serum creatinine =\< 1.5 x IULN or calculated creatinine clearance \>= 50 mL/min using the following Cockcroft-Gault Formula. This specimen must have been drawn and processed within 28 days prior to sub-study registration * Participants must have Zubrod performance status 0-1 documented within 28 days prior to sub-study registration * Participants of reproductive potential must have a negative serum pregnancy test within 28 days prior to sub-study registration * Participants must agree to have blood specimens submitted for circulating tumor DNA (ctDNA) * Participants must be offered the opportunity to participate in specimen banking and in correlative studies for collection and future use of specimens. With participant consent, specimens must be collected and submitted via the Southwest Oncology Group (SWOG) Specimen Tracking System * Participants must be informed of the investigational nature of this study and must sign and give informed consent in accordance with institutional and federal guidelines * NOTE: As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system * As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system * Participants with impaired decision-making capacity are eligible as long as their neurological or psychological condition does not preclude their safe participation in the study (e.g., tracking pill consumption and reporting adverse events to the investigator). For participants with impaired decision-making capabilities, legally authorized representatives may sign and give informed consent on behalf of study participants in accordance with applicable federal, local, and Central Institutional Review Board (CIRB) regulations Exclusion Criteria: * Participants with spinal cord compression or brain metastases must not have residual neurological dysfunction, unless no further recovery is expected, and the participant has been stable on weaning doses of corticosteroids prior to sub-study registration * Participants must not have leptomeningeal disease unless: (1) asymptomatic and (2) only detected on radiographic imaging (i.e., not present in cytology from cerebral spinal fluid \[CSF\] if CSF sampled) * Participants must not have received any prior systemic therapy (systemic chemotherapy, immunotherapy or investigational drug) within 21 days prior to sub-study registration * Participants must not have received any radiation therapy within 14 days prior to sub-study registration, with the exception of stereotactic radiation to CNS metastases which must have been completed at least 7 days prior to sub-study registration * Participants must not have received prior AMG 510 or other KRAS\^G12C specific inhibitor * Participants must not be planning to receive any concurrent chemotherapy, immunotherapy, biologic or hormonal therapy for cancer treatment while receiving treatment on this study * Participants must not have had a major surgery within 14 days prior to sub-study registration. Participant must have fully recovered from the effects of prior surgery in the opinion of the treating investigator * Participants must not have any grade III/IV cardiac disease as defined by the New York Heart Association criteria (i.e., participants with cardiac disease resulting in marked limitation of physical activity or resulting in inability to carry on any physical activity without discomfort), unstable angina pectoris, and myocardial infarction within 6 months, or serious uncontrolled cardiac arrhythmia * Participants must not have a prior or concurrent malignancy whose natural history or treatment has the potential to interfere with the safety or efficacy assessment of the investigational regimen * Participants must not have gastrointestinal disorders that may impact drug absorption * Participants must not have received strong inducers of CYP3A4 (including herbal supplements such as St. John's wort) within 14 days prior to sub-study registration and must not be planning to use strong inducers of CYP3A4 throughout protocol treatment * Participants must not have received CYP3A4 sensitive substrates (with a narrow therapeutic window) within 14 days prior to sub-study registration and must not be planning to use CYP3A4 sensitive substrates (with a narrow therapeutic window) throughout protocol treatment * Participants must not be pregnant or nursing. Participants with uteri must have agreed to use an effective contraceptive method for at least one month after the last dose of AMG 510. Participants with sperm must have agreed to use an effective contraceptive method for at least 3 months after the last dose of AMG 510. Participants are considered to be of "reproductive potential" if they have had menses at any time in the preceding 12 consecutive months and no prior oophorectomy and/or hysterectomy. In addition to routine contraceptive methods, "effective contraception" for participants with uteri also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation. Acceptable methods of birth control for participants with sperm include sexual abstinence (refraining from heterosexual intercourse); vasectomy with testing showing there is no sperm in the semen; bilateral tubal ligation or occlusion in the partner; or a condom (the female partner should also consider a form of birth control). However, if at any point a previously celibate participant chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures