Azacitidine and Entinostat in Treating Patients With Recurrent Advanced Non-Small Cell Lung Cancer

Inclusion Criteria:

* Patients must have histologically or cytologically confirmed metastatic or unresectable NSCLC
* 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 of greater than 12 weeks
* Eastern Cooperative Oncology Group (ECOG) performance status (PS) =\< 2 (Karnofsky \>= 60%)
* Leukocytes \>= 3,000/mcL
* 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
* 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-treated 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; breastfeeding should be discontinued if the mother is treated on this protocol
* Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy are ineligible