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