Targeted Treatment for Advanced Non-Small Cell Lung Cancer That Has a MET Exon 14 Skipping Gene Change (An Expanded Lung-MAP Treatment Trial)

Inclusion Criteria: * Participants must have been assigned to S1900K by the Southwest Oncology Group (SWOG) Statistics and Data Management Center (SDMC). Assignment to S1900K is determined by the LUNGMAP protocol * Participants must have documentation of NSCLC with a MET exon 14 skipping mutation determined by tissue-based or blood-based (circulating tumor DNA \[ctDNA\]) next generation sequencing (NGS) assay done within a laboratory with Clinical Laboratory Improvement Act (CLIA), International Organization for Standardization (ISO)/ International Electrotechnical Commission (IEC), College of American Pathologists (CAP), or similar certification. Documentation must either be: * NGS test results from tissue submitted for LUNGMAP screening, or * Submitted documentation in the LUNGMAP Rave Electronic Data Capture System of a MET exon 14 skipping mutation from a previously completed tissue or blood-based NGS test NOTE: Participants previously tested for and determined to have a MET exon 14 skipping mutation, outside of LUNGMAP, must also submit tissue for central Foundation Medicine (FMI) testing on the LUNGMAP screening protocol, if available * Participants must have measurable disease documented by CT or MRI. The CT from a combined positron emission tomography (PET)/CT may be used to document measurable disease ONLY if it is of diagnostic quality, otherwise, it may be used to document non-measurable disease only. Measurable disease must be assessed within 28 days prior to sub-study randomization. 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 randomization. All known sites of disease must be assessed and documented on the Baseline Tumor Assessment Form. 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 sub-study randomization to be considered measurable * 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 randomization * Participants must not have leptomeningeal disease, spinal cord compression or brain metastases unless: * Metastases have been locally treated and have remained clinically controlled and asymptomatic for at least 3 days following the stereotactic radiation and/or 14 days following whole brain radiation, and prior to sub-study randomization, AND * Participant has no residual neurological dysfunction and has been off corticosteroids for at least 24 hours prior to sub-study randomization * Participants must not have other known actionable oncogenic alterations, such as (but not limited to) EGFR sensitizing mutations, EGFR T790M mutation, ALK gene fusion, ROS1 gene rearrangement, RET gene rearrangement, NTRK rearrangement, HER2 mutation, KRAS activating mutations, and BRAF V600E mutation * Participants must have progressed (in the opinion of the treating physician) following the most recent line of therapy * Participants must have received at least one line of systemic treatment for Stage IV or recurrent NSCLC * Participants must have recovered (=\< grade 1) from any side effects of prior therapy except alopecia and vitiligo * Participants must not have received any prior systemic therapy (systemic chemotherapy, immunotherapy or investigational drug) within 21 days prior to sub-study randomization * Participants must not have received treatment with prior MET inhibitor therapies (e.g., crizotinib, tivantinib, savolitinib, tepotinib, cabozantinib, and foretinib). * Participants must not have received treatment with prior angiogenesis inhibitor therapies (including but not limited to bevacizumab and ramucirumab) * Participants must not have a history of interstitial lung disease that required steroid treatment * Participants must not have received any radiation therapy within 7 days prior to sub-study randomization with the exceptions of * Stereotactic radiation to CNS metastases which must have been completed at least 3 days prior to sub-study randomization and * Palliative radiotherapy to bone metastases which must have been completed at least 1 day prior to sub-study randomization * 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 randomization. Participants must have fully recovered from the effects of prior surgery in the opinion of the treating investigator * Participants must not have a prior or concurrent malignancy whose natural history or treatment (in the opinion of the treating physician) has the potential to interfere with the safety or efficacy assessment of the investigational regimen * Participants must be able to swallow tablets whole * Absolute neutrophil count \>= 1.5 x 10\^3/uL (within 28 days prior to sub-study randomization) * Hemoglobin \>= 9.0 g/dL (within 28 days prior to sub-study randomization) * Platelets \>= 100 x 10\^3/uL (within 28 days prior to sub-study randomization) * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) unless history of Gilbert's disease. Participants with history of Gilbert's disease must have total bilirubin =\< 5 x institutional ULN (within 28 days prior to sub-study randomization) * Aspartate aminotransferase (AST) and Alanine aminotransferase (ALT) =\< 2.5 × institutional ULN. Participants with history of liver metastasis must have AST =\< 5 x ULN (within 28 days prior to sub-study randomization) * Participants must have a serum creatinine =\< the institutional upper limit of normal (IULN) or calculated creatinine clearance \>= 30 mL/min using the following Cockcroft-Gault Formula. This specimen must have been drawn and processed within 28 days prior to sub-study randomization * Participants must have a cystatin C test performed to obtain baseline value within 28 days prior to sub-study randomization * Participants' most recent Zubrod performance status must be 0-1 and be documented within 28 days prior to sub-study randomization * Participants must have a completed medical history and physical exam within 28 days prior to sub-study randomization * Participants must have adequate cardiac function. Participants with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, must have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, participants must be class 2B or better * Participants with known human immunodeficiency virus (HIV)-infection must be on effective anti-retroviral therapy and have undetectable viral load test on the most recent test results obtained within 6 months prior to sub-study randomization * Participants with evidence of chronic hepatitis B virus (HBV) infection must have undetectable HBV viral load while on suppressive therapy on the most recent test results obtained within 6 months prior to sub-study randomization, if indicated * Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. Participants currently being treated for HCV infection must have undetectable HCV viral load test on the most recent test results obtained within 6 months prior to sub-study randomization, if indicated by the treating investigator * Participants must not have cirrhosis at a level of Child-Pugh B (or worse) OR any degree of cirrhosis AND a history of hepatic encephalopathy or clinically meaningful ascites resulting from cirrhosis * Participants must not have grade \< 0 of peripheral edema within 28 days prior to sub-study randomization * Participants must not have experienced any arterial thromboembolic events, including but not limited to transient ischemic attack or cerebrovascular accident within 6 months prior to sub-study randomization * Participants must not have uncontrolled blood pressure and hypertension within 28 days prior to sub-study randomization * Participants must not be pregnant or breastfeeding (nursing includes breast milk fed to an infant by any means, including from the breast, milk expressed by hand, or pumped). Individuals who are of reproductive potential must have agreed to use an effective contraceptive method with details provided as a part of the consent process. A person who has had menses at any time in the preceding 12 consecutive months or who has semen likely to contain sperm is considered to be of "reproductive potential." In addition to routine contraceptive methods, "effective contraception" also includes refraining from sexual activity that might result in pregnancy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) including hysterectomy, bilateral oophorectomy, bilateral tubal ligation/occlusion, and vasectomy with testing showing no sperm in the semen * Participants must have a Lymphoscintigraphy scan performed within 28 days prior to sub-study randomization * Participants must also be offered participation in specimen banking. With participant consent, specimens must be collected and submitted via the 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