Capmatinib Plus Trametinib for the Treatment of Metastatic Non-small Cell Lung Cancer With MET Exon 14 Skipping Mutation

Inclusion Criteria: * Participants must have histologically or cytologically confirmed, non-small cell lung cancer. * Documented MET exon 14 skipping mutation by tumor DNA sequencing or cell-free DNA assay by Clinical Laboratory Improvement Act (CLIA) - approved laboratory AND previously received treatment with a MET inhibitor (capmatinib crizotinib, savolitinib, or tepotinib) with evidence of disease progression, in the opinion of the investigator. * Note - MET inhibitor therapy is NOT required to be the most recent anti-cancer therapy. Prior treatment with platinum-based chemotherapy or anti-programmed cell death protein 1 (PD-1) /programmed death-ligand 1 (PD-L1) therapy (alone or in combination with chemotherapy) is allowed, but not required. * \- or (For dose escalation only): MET amplification or fusion detected in tumor sample or cell-free DNA by next generation sequencing (NGS) or Fluorescent in situ hybridisation (FISH) by CLIA-approved laboratory AND prior treatment with a MET inhibitor (capmatinib crizotinib, savolitinib, or tepotinib) with at least 5 months of clinical benefit, followed by disease progression, in the opinion of the investigator. * Archived tissue available or willingness to undergo new tumor biopsy. * Measurable disease defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria. * Life expectancy of at least 3 months. * Age \>= 18 years. * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1 (Karnofsky) \> 60%. * Resolution of all acute toxic effects (other than alopecia, or non-clinically significant lab abnormalities) of prior chemotherapy, targeted therapy, immunotherapy, radiotherapy, or surgical procedures to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) Version 5.0 grade 1. * Absolute neutrophil count \>= 1,500/microliter (mcL) * Platelets \>= 100,000/mcL * Hemoglobin (Hgb) \>= 9 g/dl * Total bilirubin within 1.2 X institutional upper limit of normal, unless elevated due to Gilbert's syndrome and direct bilirubin is within normal limits. * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase (SGOT)) =\< 3 X institutional upper limit of normal if no known liver metastases. * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase (SGPT)) =\< 3 X institutional upper limit of normal if no known liver metastases. * Alkaline phosphatase (ALP) =\< 5.0 X institutional upper limit of normal. * Creatinine =\< 1.5 x within institutional upper limit of normal. * Creatinine glomerular filtration rate (GFR) \>= 30 mL/min/1.73 m\^2,calculated using the Cockcroft-Gault equation, unless data exists supporting safe use at lower kidney function values, no lower than 30 mL/min/1.73 m\^2. * Asymptomatic serum amylase =\< grade 2. * Asymptomatic serum amylase increase grade 1 and 2 are allowed if at the beginning of the study is confirmed to have no signs and/or symptoms suggesting pancreatitis or pancreatic injury (e.g., elevated P-amylase, abnormal imaging findings of pancreas, etc.) * Serum lipase =\< upper limits of normal (ULN). * Ability to understand a written informed consent document, and the willingness to sign it. * For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. * Individuals with a history of hepatitis C virus (HCV) infection must have been treated and cured or currently be on treatment with an undetectable HCV viral load. * Individuals with treated brain metastases are eligible if follow-up brain imaging (within 1 month prior to first dose) after central nervous system (CNS)-directed therapy shows no evidence of progression and not on steroids. * Individuals with a prior or concurrent malignancy are eligible for this trial as long as they are not on active treatment and no active disease is present, and whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen. Exceptions: thyroid hormone replacement is allowed and adjuvant hormonal therapy for breast cancer is allowed. * Women of child-bearing potential and men with partners of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 16 weeks after last administration of study treatment. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 16 weeks after last administration of study treatment. Exclusion Criteria: * Known activating mutations or oncogenic fusions in Epithelial Growth Factor Receptor (EGFR), KRAS g12c, ALK, ROS1, Neurotrophic tyrosine receptor kinase (NTRK), BRAF V600E, or RET or known on-target MET mutations on residues D1228 or Y1230. * For Phase I patients enrolling into dose levels 1 or -1, intolerability of prior treatment with capmatinib 300 mg BID requiring dose reduction or permanent discontinuation is exclusionary. * For Phase I patients enrolling into dose level -2, intolerability of prior treatment with capmatinib 200 mg BID requiring dose reduction or permanent discontinuation is exclusionary. * For Phase I patients enrolling into dose level 2, intolerability of prior treatment with capmatinib 400 mg BID requiring dose reduction or permanent discontinuation is exclusionary. * Phase Ib patients enrolling into the dose expansion cohort must have previously tolerated the RP2D of capmatinib if they have received prior capmatinib treatment. * Pregnant women are excluded from this study because capmatinib and trametinib are tyrosine kinase inhibitors (TKIs) with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with capmatinib and trametinib, breastfeeding should be discontinued if the mother is treated with capmatinib and trametinib. * Patients who have received systemic anti-cancer therapies within the following time periods prior to the first dose of study drug: within 3 weeks of cytotoxic chemotherapy or antibody therapy, radiation within 2 weeks, targeted therapy within 7 days. * Note: Concomitant administration of Luteinizing hormone-releasing hormone (LHRH) analogues for prostate cancer and somatostatin analogues for neuroendocrine tumors are allowed as per standard of care. Patients who are currently receiving and progressing on capmatinib monotherapy will be allowed to continue treatment without interruption * History of interstitial lung disease or pneumonitis. * Note: History of radiation pneumonitis not requiring steroids is allowed. * Known Hepatitis B Virus (HBV), Hepatitis C Virus (HCV) infection, or human immunodeficiency virus (HIV) with inadequate CD4+ T cell counts or a history of acquired immunodeficiency syndrome (AIDS)-defining opportunistic infections. * Note: Participants with laboratory evidence of cleared HBV and HCV infection will be permitted). Patients living with HIV, with adequate CD4+ T cell counts, and without a history of AIDS-defining opportunistic infections will be permitted. * Known active COVID-19 infection. * Note: Patients who have recovered from an infection and test negative for viral ribonucleic acid (RNA) will be allowed. * History or evidence of cardiovascular risk including any of the following: * Left ventricular ejection fraction (LVEF) \< lower limit of normal (LLN) by echocardiogram (ECHO) or multigated acquisition scan (MUGA). * A QT interval corrected for heart rate using the Fridericia's formula (QTcF) 470 msec. * History or evidence of current clinically significant uncontrolled arrhythmias. * History of acute coronary syndromes (including myocardial infarction and unstable angina), coronary angioplasty, or stenting within 6 months prior to study enrollment. * History or evidence of current \>= Class II congestive heart failure as defined by New York Heart Association (NYHA). * Treatment refractory hypertension defined as a blood pressure of systolic \> 150 mmHg and/or diastolic \> 95 mm Hg which cannot be controlled by anti-hypertensive therapy. * Patients with intra-cardiac defibrillators. * Note: Participants with atrial fibrillation controlled (defined as not requiring change in cardiac drug dosing, emergency room visit, or hospital admission) for \>30 days prior to dosing are eligible. * Is currently receiving any other investigational agents. * Hypersensitivity to capmatinib or trametinib or any of its excipients. * Patients with known history or current evidence of retinal vein occlusion (RVO) or retinal pigment epithelial detachment (RPED). * Major surgery (e.g., intra-thoracic, intra-abdominal or intra-pelvic) within 4 weeks prior (2 weeks for resection of brain metastases) to starting study treatment or who have not recovered from side effects of such procedure. * Note: Video-assisted thoracic surgery (VATS) and mediastinoscopy will not be counted as major surgery and participants can be enrolled in the study \>= 1 week after the procedure. * Participants receiving treatment with strong inducers of CYP3A that cannot be discontinued at least 1 week prior to the start of treatment with study treatment and for the duration of the study. * Any condition that in the opinion of the investigator would interfere with the participant's safety or compliance while on trial.