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