Study of Ponatinib in Patients With Lung Cancer Preselected Using Different Candidate Predictive Biomarkers

Inclusion Criteria: * PART A: Patients must have histologically or cytologically confirmed locally advanced (after failure of local therapy) or metastatic lung cancer (any histology, except carcinoid) stage IIIa, IIIb or IV * PART A: Existing formalin fixed paraffin embedded biopsy of the lung cancer with potentially sufficient material for analysis * PART A: Non-small cell lung cancer (NSCLC) with adenocarcinoma histology must have been previously tested for both epidermal growth factor receptor (EGFR) mutations and anaplastic lymphoma kinase (ALK) rearrangements * PART A: Able (physically and financially) to travel to University of Colorado for clinical trial treatment * PART B: Patients must have histologically or cytologically confirmed locally advanced (after failure of local therapy) or metastatic lung cancer (any histology, except carcinoid) stage IIIa, IIIb or IV * PART B: Patients must be proven to meet marker criteria (FGFR1 silver in situ hybridization (SISH) + in situ hybridization (ISH) +, FGFR1 SISH+ ISH negative \[-ve\], FGFR1 SISH-ve ISH+, FGFR1 SISH-ve ISH-ve \[FGFR1 double negative cohort\] or ret proto-oncogene \[RET\] FISH+) prior to enrollment into Part B (treatment); adenocarcinoma patients must be known to not possess either an EGFR mutation or an ALK rearrangement in their tumor (if positive for one, testing for both is not required) * PART B: Patients must have measurable disease as per Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1 * PART B: Patients may have received any number of lines of prior therapy * PART B: Life expectancy of \>= 3 months * PART B: Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%) * PART B: Leukocytes \>= 3,000/mcL * PART B: Absolute neutrophil count \>= 1,500/mcL * PART B: Hemoglobin \>= 9 g/dL * PART B: Platelets \>= 100,000/mcL * PART B: Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN), unless due to Gilbert's syndrome * PART B: Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN * PART B: Creatinine =\< 1.5 X ULN OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * PART B: Serum lipase =\< 1.5 X ULN * PART B: Serum amylase =\< 1.5 X ULN * PART B: Previous treatment related side-effects/adverse events must have resolved to at least grade 1 or, at the discretion of the investigator, select stable grade 2 toxicities (e.g. alopecia or fatigue) may be permissible if unchanging in grade for at least 3 months following discussion with the principal investigator (PI) * PART B: Patients with central nervous system (CNS) metastases are eligible for enrollment if they have no overt evidence of neurological deficits, and are not requiring anti-epileptics or steroids to control their neurological symptoms; patients with known CNS metastases must have relevant CNS imaging performed approximately coincident with body imaging during response assessments * PART B: The effects of ponatinib on the developing human fetus are unknown; for this reason women of child-bearing potential must have a negative urine or blood pregnancy test at screening for Part B; women of child-bearing potential and men must also have documented agreement to use adequate contraception (hormonal or barrier method of birth control; abstinence) from the time of screening until 30 days after the end of study treatment; should a woman become pregnant or suspect she is pregnant while she or her partner are participating in this study, they should inform the treating physician immediately * PART B: Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * PART A: Known EGFR mutation and/or ALK rearrangement in NSCLC with adenocarcinoma histology * PART B: No previous treatment with a standard or investigational anti-cancer agent within predicted 5 half-lives of the agent; or 28 days whichever is the shorter; if the plasma half-life is not known or the previous therapy was a monoclonal antibody then a 28 day washout period will be considered as the default requirement * PART B: No previous or current exposure to other FGFR inhibitors in the FGFR-selected cohorts, or RET inhibitors in the RET selected cohorts * PART B: Prior radiotherapy to proposed target lesions is not permitted unless completed more than 4 weeks prior to treatment within the study and that there has been documented progression at these sites; radiotherapy to non-target lesions is permitted within 2 weeks of study entry provided all acute effects of the radiotherapy have resolved to =\< grade 1 * PART B: History of allergic or severe reactions attributed to compounds of similar chemical or biologic composition to ponatinib * PART B: Ponatinib is a substrate for cytochrome P450, family 3, subfamily A, polypeptide 4/5 (CYP3A4/5), concurrent use with potent CYP3A4/5 inhibitors or inducers should be undertaken with caution * PART B: History of clinically significant bleeding disorder * PART B: History of acute pancreatitis within 1 year of study or history of chronic pancreatitis * PART B: Uncontrolled hypertriglyceridemia (triglycerides \> 450 mg/dL) * PART B: Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection requiring intravenous antibiotics * Psychiatric illness/social situations that would limit compliance with study requirements * Congestive heart failure, unstable angina pectoris, or myocardial infarction within the 3 months prior to enrollment in part B of the study * History of clinically significant (as determined by the treating medical doctor \[MD\]) cardiac arrhythmia (atrial or ventricular) * PART B: Patients who have had major surgery within 28 days prior to entering the study or those who have not recovered from adverse events \> grade 1 relating to the surgery * PART B: Pregnant or breastfeeding women * PART B: Patients with inability to take oral medications, or, in the investigator's opinion, gastrointestinal conditions or abnormalities likely to influence the absorption of oral medications * PART B: Concomitant use of medications known to be associated with torsades-de-pointes