Inclusion Criteria:

          -  Patients must have histologically or cytologically proven primary non-squamous
             non-small cell lung cancer (adenocarcinoma, large cell carcinoma, adenocarcinoma in
             situ, mixed histology with < 50% squamous or unspecified); patients with tumors having
             squamous cell components >= 50% are not eligible; disease must be stage IV

          -  Patients must have documented ALK positivity at the time of initial crizotinib
             monotherapy using the Vysis Break-Apart FISH assay (or other Food and Drug
             Administration [FDA]-approved diagnostic test); samples are deemed to be FISH-positive
             if greater than or equal to 15% of scored tumor cells had split ALK 5' and 3' probe
             signals or had isolated 3' signal; FISH status must be documented on the Onstudy Form
             and a copy of the pathology report from the Vysis Break-Apart FISH assay (or other
             FDA-approved diagnostic test) must be submitted

          -  Prior to registration, patients must have achieved clinical benefit with crizotinib
             monotherapy and subsequently have systemically progressed; clinical benefit is defined
             as having stable disease on crizotinib monotherapy for at least 90 days or achieving a
             confirmed partial or complete response; systemic progression is defined as progressive
             disease based on Response Evaluation Criteria in Solid Tumors (RECIST) version 1.1,
             excluding progression based on brain/CNS metastases alone

          -  Patients must have received crizotinib monotherapy at 250 mg BID on a continuous
             dosing schedule for at least 90 days; patients must be planning to start treatment at
             least three days, but no more than 30 days after discontinuing crizotinib monotherapy;
             patients who were not able to tolerate 250 mg BID of crizotinib are not eligible for
             this study

          -  Patients must be pemetrexed-naïve; patients may have received any number of prior
             chemotherapy or molecularly targeted agents; if crizotinib was used in the 1st line
             setting then chemotherapy naive patients are also eligible; if patient received
             crizotinib in combination with chemotherapy, prior chemotherapy must have been
             discontinued at least 14 days prior to registration and all adverse events must have
             resolved to =< grade 1

          -  Patients must have measurable disease per RECIST documented by computed tomography
             (CT) or magnetic resonance imaging (MRI); the CT from a combined positron emission
             tomography (PET)/CT may be used to document only non-measurable disease unless it is
             of diagnostic quality; measurable disease must be assessed within 28 days prior to
             registration; 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 registration; all disease must be assessed and documented on the
             Baseline Tumor Assessment Form RECIST 1.1

          -  Patients must have a CT or MRI scan of the brain to evaluate for CNS disease within 42
             days prior to registration; patient must not have brain metastases unless: (1)
             metastases have been treated and have remained controlled for at least 14 days
             following treatment or was not treated, but is asymptomatic, AND (2) patient has no
             residual neurological dysfunction off corticosteroids or anti-convulsants for at least
             14 days

          -  Patients may have received palliative radiotherapy to non-target lesions within 14
             days prior to registration provided all radiotherapy related toxicities have resolved
             to =< grade 1 prior to registration; patients must not have received any major surgery
             within 28 days prior to registration

          -  Patients must not have had any prior exposure to heat shock protein (HSP)90 inhibitors
             (such as IPI-504 or ganetespib) or non-crizotinib ALK inhibitors (such as AP26113 or
             LDK378)

          -  Patients must be offered participation in the translational medicine studies;
             additionally if patient has biopsy accessible disease they must be offered
             participation in the translational medicine studies

          -  Absolute neutrophil count (ANC) >= 1,500/ul

          -  Platelet count >= 100,000/ul

          -  Hemoglobin >= 9 g/dL

          -  Serum bilirubin =< 2 X institutional upper limit of normal (IULN)

          -  Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase [AST]) or
             serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase [ALT]) =< 2.5 x
             IULN

          -  Estimated (calculated) or measured glomerular filtration rate >= 45 mL/min (or 45
             mL/min/1.73 m^2); creatinine (mg/dl) used in calculation (Cockroft-Gault) must be
             obtained within 28 days prior to registration

          -  Male patients must have free and total testosterone level obtained within 28 days
             prior to registration

          -  Pre-study history and physical must be obtained with 28 days prior to registration

          -  Patients must have Zubrod performance status 0-2 within 28 days prior to registration

          -  Patients must be able to swallow capsules

          -  Patients must have corrected QT (QTC) interval =< 480 msec on electrocardiogram (EKG)
             at baseline; patient with congenital long QT syndrome are not eligible

          -  No other prior malignancy is allowed except for the following: adequately treated
             basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated
             stage I or II cancer from which the patient is currently in complete remission, or any
             other cancer from which the patient has been disease free for five years

          -  Patients must not be pregnant or nursing; women/men of reproductive potential must
             have agreed to use an effective contraceptive method; a woman is considered to be of
             "reproductive potential" if she has had menses at any time in the preceding 12
             consecutive months; in addition to routine contraceptive methods, "effective
             contraception" also includes heterosexual celibacy and surgery intended to prevent
             pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy,
             bilateral oophorectomy or bilateral tubal ligation; however, if at any point a
             previously celibate patient chooses to become heterosexually active during the time
             period for use of contraceptive measures outlined in the protocol, he/she is
             responsible for beginning contraceptive measures

          -  REGULATORY CRITERIA: Patients or their legally authorized representative must be
             informed of the investigational nature of this study and must sign and give written
             informed consent in accordance with institutional and federal guidelines

          -  REGULATORY CRITERIA: As a part of the Oncology Patient Enrollment Network (OPEN)
             registration process the treating institution's identity is provided in order to
             ensure that the current (within 365 days) date of institutional review board approval
             for this study has been entered in the system

          -  CROSSOVER (STEP 2) REGISTRATION: Patients must have progressed systemically on Arm 2
             of this study (pemetrexed monotherapy)

          -  CROSSOVER (STEP 2) REGISTRATION: Patients must be registered to crossover (Step 2)
             within 30 days of discontinuing treatment on Arm 2 of this study

          -  CROSSOVER (STEP 2) REGISTRATION: ANC >= 1,500/ul

          -  CROSSOVER (STEP 2) REGISTRATION: Platelet count >= 100,000/ul

          -  CROSSOVER (STEP 2) REGISTRATION: Serum bilirubin =< 2 X IULN

          -  CROSSOVER (STEP 2) REGISTRATION: SGOT (AST) or SGPT (ALT) =< 2.5 x IULN

          -  CROSSOVER (STEP 2) REGISTRATION: estimated (calculated) or measured glomerular
             filtration rate >= 45 mL/min (or 45 mL/min/1.73 m^2) within 28 days prior to
             registration; creatinine (mg/dl) used in calculation (Cockroft-Gault) must be obtained
             within 28 days prior to registration

          -  CROSSOVER (STEP 2) REGISTRATION: male patients must have free and total testosterone
             level obtained within 28 days prior to Crossover (Step 2) Registration

          -  CROSSOVER (STEP 2) REGISTRATION: patients must have Zubrod performance status 0-2
             within 28 days prior to Crossover (Step 2) Registration