INC280 and Erlotinib Hydrochloride in Treating Patients With Non-small Cell Lung Cancer

Inclusion Criteria: * Patients must provide written informed consent prior to any screening procedures * Willing and able to comply with scheduled visits, treatment plan and laboratory tests * Patient is able to swallow and retain oral medication * Histologically or cytologically documented diagnosis of NSCLC * Must have evidence of MET expression by fluorescence in situ hybridization (FISH), MET immunohistochemistry (IHC) score of 2-3+, reverse-transcriptase polymerase chain reaction (RT-PCR) or a mutation * Tumor tissue for correlative studies is mandatory * Patients in expansion cohort A will have a biopsy (which is standard of care) at the time of progression that shows evidence of MET positivity and meets the criteria for acquired resistance per the Jackman criteria * Previously received treatment with a single-agent erlotinib * A tumor that harbors an EGFR mutation known to be associated with drug sensitivity (i.e. G719X, exon 19 deletion, L858R, L861Q) * Systemic progression of disease (Response Evaluation Criteria in Solid Tumors \[RECIST\] or World Health Organization \[WHO\]) while on continuous treatment with gefitinib or erlotinib * Patients must have measurable disease; disease in previously irradiated sites is considered measurable if there is clear disease progression following radiation therapy * Failed 1-2 prior chemotherapies for advanced disease; prior erlotinib is allowed in the dose finding phase and expansion cohort A (Patients in expansion cohort B must be erlotinib naïve and have v-Ki-ras2 Kirsten rat sarcoma viral oncogene homolog \[KRAS\] wild type tumor) * Patients must be willing to be off therapy for a minimum of two weeks (In expansion cohort A patients on erlotinib do not have to discontinue treatment) * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Life expectancy greater than 3 months * Hemoglobin \> 9 g/dL (International System \[SI\] units: 90 g/L) without transfusion support or growth factors within 10 days of starting INC280 * Platelet count \>= 75 x 10\^9/L * Absolute neutrophil count (ANC) \>= 1.2 x 10\^9/L without growth factor support * Total bilirubin =\< 2 x upper limit of normal (ULN) * Aspartate aminotransferase (AST)/serum glutamic oxaloacetic transaminase (SGOT) and/or alanine aminotransferase (ALT)/serum glutamate pyruvate transaminase (SGPT) =\< 2.5 x upper limit of normal (ULN) * Serum creatinine =\< 2 x ULN * Serum amylase =\< ULN * Serum lipase =\< ULN * Fasting serum triglyceride level =\< 500 mg/dL Exclusion Criteria: * Patients who have had major surgery within 4 weeks of initiation of study medication, excluding the placement of vascular access * Patients with concurrent uncontrolled medical conditions that may interfere with their participation in the study or potentially affect the interpretation of the study data * Unstable angina pectoris, symptomatic congestive heart failure, myocardial infarction =\< 6 months prior to first study treatment, serious uncontrolled cardiac arrhythmia * Severely impaired lung function * Active (acute or chronic) or uncontrolled infection * Nonmalignant medical illnesses that are uncontrolled or whose control may be jeopardized by the treatment with the study therapy * Liver disease (i.e. cirrhosis, chronic active hepatitis, chronic persistent hepatitis) * Symptomatic central nervous system (CNS) metastases that are neurologically unstable or requiring increasing doses of steroids to control CNS disease * Note: Patients with controlled CNS metastases are allowed; radiotherapy or surgery for CNS metastases must have been completed \> 2 weeks prior to study entry; patients must be neurologically stable, having no new neurologic deficits on clinical examination, and no new findings on CNS imaging; steroid use for management of CNS metastases must be at a stable dose for two weeks preceding study entry * Receiving drugs known to be strong inducers of cytochrome P450 3A4 (CYP3A4) or inhibiting drugs known to interact with erlotinib including, but not limited to: enzyme-inducing anticonvulsants, rifampicin, rifabutin, St John wort and ketoconazole * Treatment with proton pump inhibitors within 3 days prior to study entry * Currently receiving any prohibited medications including vitamins and herbal supplements * Any other condition that would, in the investigator's judgment, contraindicate participation in the clinical study due to safety concerns or compliance with clinical study procedures, e.g., infection/inflammation, intestinal obstruction, unable to swallow medication, social/ psychological issues, etc. * Pregnant or nursing (lactating) women, where pregnancy is defined as the state of a female after conception and until the termination of gestation, confirmed by a positive human chorionic gonadotropin (hCG) laboratory test (\> 5 mIU/mL) * Women of child-bearing potential, defined as all women physiologically capable of becoming pregnant, unless they are using highly effective methods of contraception during dosing and for 3 months after stopping study drug; highly effective contraception methods include: * Total abstinence or * Male or female sterilization or * Combination of any two of the following (a+b or a+c or b+c): * (a) Use of oral, injected or implanted hormonal methods of contraception * (b) Placement of an intrauterine device (IUD) or intrauterine system (IUS) * (c) Barrier methods of contraception: condom or occlusive cap (diaphragm or cervical/vault caps) with spermicidal foam/gel/film/cream/vaginal suppository * Women are considered post-menopausal and not of child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks ago; in the case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child bearing potential * Sexually active males must use a condom during intercourse while taking the drug and for 3 months after stopping study drug and should not father a child in this period; a condom is required to be used also by vasectomized men in order to prevent delivery of the drug via seminal fluid * Patients unwilling or unable to comply with the protocol * Prior treatment with a MET inhibitor or hepatocyte growth factor (HGF) targeting agent * No history of another active cancer * Human immunodeficiency virus (HIV) seropositivity