Inclusion Criteria:

- Histologically or cytologically confirmed non-small cell lung cancer (NSCLC):

- Metastatic or unresectable disease

- Patient must have failed at least one previous chemotherapy regimen

- Patients must have measurable disease, defined as at least one lesion that can be
accurately measured in at least one dimension (longest diameter to be recorded) as >=
20 mm with conventional techniques or as >= 10 mm with spiral computed tomography
(CT) scan

- Life expectancy > 12 weeks

- Leukocytes >= 3,000/mcL

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

- Absolute neutrophil count >= 1,500/mcL

- Platelet count >= 100,000/mcL

- Total bilirubin within normal institutional limits

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

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

- The effects of entinostat and 5-AZA on the developing human fetus at the recommended
therapeutic dose are unknown; for this reason, 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
participating in this study, she should inform her treating physician immediately

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

- Patients who have a major objective response to treatment on this protocol, and who
experience progression of disease at least 1 year after completion of protocol
consent and therapy, may be re- retreated at the previously effective dose and
schedule

Exclusion Criteria:

- Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for
nitrosoureas or mitomycin C) prior to entering the study or those who have not
recovered from adverse events due to agents administered more than 4 weeks earlier

- Patients may not be receiving any other investigational agents

- Patients with uncontrolled brain metastases; patients with brain metastases must have
stable neurologic status following local therapy (surgery or radiation) for at least
4 weeks, and must be without neurologic dysfunction that would confound the
evaluation of neurologic and other adverse events

- Patients with liver metastases that replace greater than 30% of the liver parenchyma

- History of allergic reactions attributed to compounds of similar chemical or biologic
composition to entinostat, 5-AZA, mannitol or other agents used in the study

- 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 because entinostat and 5-AZA are agents
with the potential for teratogenic or abortifacient effects; because there is an
unknown but potential risk for adverse events in nursing infants secondary to
treatment of the mother with entinostat or 5-AZA, breastfeeding should be
discontinued if the mother is treated on this protocol; these potential risks may
also apply to other agents used in this study

- Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral
therapy are ineligible because of the potential for pharmacokinetic interactions with
entinostat or 5-AZA; in addition, these patients are at increased risk of lethal
infections when treated with marrow-suppressive therapy