Inclusion Criteria:

- PHASE I: Patients must have metastatic/recurrent, histologically confirmed NSCLC that
harbors an EGFR activating mutation (Exon 21 L858R, Exon 19 deletion, Exon 18 G719X,
Exon 21 L861Q) with progressive disease by RECIST 1.1 on a previous EGFR-tyrosine
kinase inhibitor (TKI) or; patients must have metastatic/recurrent histologically
confirmed NSCLC that harbors an EGFR Exon 20 insertion with progressive disease on
platinum containing chemotherapy

- PHASE II COHORT A: Patients must have metastatic/recurrent histologically confirmed
NSCLC that harbors an EGFR activating mutation (Exon 21 L858R, Exon 19 deletion, Exon
18 G719X, Exon 21 L861Q) with stable disease by RECIST 1.1 as best response on
erlotinib compared to pre-treatment erlotinib imaging by RECIST 1.1 or progressive
disease compared to pre-treatment imaging by RECIST 1.1; patients must be enrolled
within 6 months of initiation of erlotinib

- PHASE II COHORT B: Patients must have metastatic/recurrent histologically confirmed
NSCLC that harbors an EGFR Exon 20 insertion with progressive disease on platinum
doublet chemotherapy

- FOR PHASE I: if patient is on erlotinib at the time of signed consent, the patient
does not need to be discontinued prior to initiation of erlotinib and AT13387; other
EGFR-TKIs must be discontinued at least 7 days prior to initiation of erlotinib and
AT13387

- FOR PHASE II COHORT A: If patient is on erlotinib at the time of signed consent,
erlotinib does not need to be discontinued prior to receiving treatment erlotinib and
AT13387; last dose of erlotinib must be less than 28 days from when patient signs
consent

- FOR PHASE II COHORT B: (EGFR Exon 20 Insertions): Prior EGFR-TKIs including erlotinib
is allowed; if patient is on erlotinib at the time of signed consent, erlotinib does
not need to be discontinued prior to initiation of erlotinib and AT13387

- Local testing for EGFR-mutations for this study is acceptable provided it was
performed in a Clinical Laboratory Improvement Amendment (CLIA) certified lab

- Patients with a prior history of brain metastases are eligible provided:

- The brain metastases have been treated

- The patient is asymptomatic from the brain metastases

- Corticosteroids prescribed for the management of brain metastases have been
discontinued at least 7 days prior to registration

- Patients must have completed last chemotherapy >= 3 weeks or radiotherapy >= 2 weeks
prior to receiving study drugs

- Patients must have recovered from adverse events attributable to previous treatment
to =< grade 1, except for alopecia and sensory neuropathy =< grade 2

- Patients must have the ability to swallow tablets

- Measurable disease by RECIST 1.1

- Eastern Cooperative Oncology Group (ECOG) performance status =< 2 (Karnofsky >= 60%)

- Life expectancy of greater than 3 months

- Leukocytes >= 3,000/mcL

- Absolute neutrophil count >= 1,500/mcL

- Platelets >= 100,000/mcL

- Total bilirubin within normal institutional limits

- Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase
[SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
=< 2.5 x institutional upper limit of normal

- Creatinine within normal institutional limits OR creatinine clearance >= 60
mL/min/1.73 m^2 for patients with creatinine levels above institutional normal

- Women of child-bearing potential and men must agree to use adequate contraception
(hormonal or barrier method of birth control; abstinence) prior to study entry and
for the duration of study participation; 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 4 months after completion of erlotinib and/or AT13387
administration

- Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

- Patients who are receiving any other investigational agents

- History of allergic reactions attributed to compounds of similar chemical or biologic
composition to erlotinib and/or AT13387

- History of pneumonitis attributed to an EGFR inhibitor; history of radiation
pneumonitis is allowed provided steroid administration for pneumonitis was not
required

- Strong cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP3A4) inducers and
inhibitors should be avoided; selection of alternate concomitant medications with no
or minimal CYP3A4 enzyme inhibition potential is recommended; as part of the
enrollment/informed consent procedures, the patient will be counseled on the risk of
interactions with other agents, and what to do if new medications need to be
prescribed or if the patient is considering a new over-the-counter medicine or herbal
product

- Uncontrolled intercurrent illness including, but not limited to, ongoing or active
infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
arrhythmia, or psychiatric illness/social situations that would limit compliance with
study requirements

- Pregnant women are excluded from this study; breastfeeding should be discontinued if
the mother is treated with erlotinib and AT13387

- Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral
therapy are ineligible

- Prior treatment with a Hsp90 inhibitor

- Treatment with proton pump inhibitors within 3 days prior to study entry; H2-blockers
are allowed by should be spaced 12 hours apart from erlotinib administration

Minimum Eligible Age: 18 Years

Maximum Eligible Age: N/A

Eligible Gender: Both