Phase II Anti-PD1 Epigenetic Therapy Study in NSCLC.

Inclusion Criteria: * Patients must have histologically proven stage IIIB, IV or recurrent non-small cell lung cancer. Patients must be willing to undergo a pre-treatment biopsy, either core needle biopsy or equivalent amount or via excisional specimen. (cytology specimen not acceptable for this purpose). * 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 for non-nodal lesions and short axis for nodal lesions) as \>20 mm with conventional techniques or as \>10 mm with spiral CT scan, MRI, or calipers by clinical exam. See Section 11 for the evaluation of measurable disease. A CT scan of the abdomen and pelvis is not required for patients with no disease in these areas. * Age \>18 years. Because no dosing or adverse event data are currently available on the use of azacitidine with entinostat, or of Nivolumab, in patients \<18 years of age, children are excluded from this study. * Eastern Cooperative Oncology Group (ECOG) performance status 0 to 1. * Life expectancy of greater than 12 weeks. * Patients must have adequate organ and marrow function. * The effects of entinostat, azacitidine, and Nivolumab, on the developing human fetus 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 and for up to 23 weeks after the last dose of nivolumab. 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 who are sexually active with women of childbearing potential must also use an adequate contraceptive method for up to 31 weeks after fhe last dose of nivolumab. * Ability to understand and the willingness to sign a written informed consent document. * All adenocarcinoma patients must be tested for ALK rearrangements and EGFR (Exon 19 Deletion and Exon 21 L8585R Substitution) mutations and must have been treated with EGFR or ALK TKI therapy if found to have an actionable alteration. If patients are KRAS positive, testing for ALK rearrangements and EGFR mutations is not applicable. * All patients should have been offered a platinum-based chemotherapy. For EGFR/ALK wild type patients, no more than two prior chemotherapy-based lines of therapy for advanced or metastatic NSCLC is permitted. For EGFR mutated or ALK translocated patients, no more than three prior lines of therapy for advanced or metastatic NSCLC is permitted. Patients who refuse platinum based chemotherapy, may be allowed to enroll if they meet all other criteria. * Patients who received adjuvant or neoadjuvant platinum-doublet chemotherapy (after surgery and/or radiation therapy) and developed recurrent or metastatic disease within 6 months of completing therapy are eligible and the adjuvant or neoadjuvant chemotherapy will count as a line of therapy as above. * Subjects with recurrent disease \> 6 months after adjuvant or neoadjuvant platinum-based chemotherapy, who also subsequently progressed during or after a platinum-doublet regimen given to treat the recurrences, are eligible and do not count as another line of therapy for advanced disease. * Subjects who received pemetrexed, bevacizumab, or erlotinib as maintenance therapy (nonprogressors with platinum-based doublet chemotherapy) and subsequently progressed after maintenance therapy, are eligible and do not count as a line of therapy. However, subject who received a tyrosine kinase inhibitor after failure of a prior platinum-based therapy, that tyrosine kinase inhibitor therapy would count as an additional line of therapy. * Patients who have been treated with prior standard of care PD-1/L1 agents, alone or in combination with chemotherapy, are eligible. Patients previously treated on clinical trials with non PD-1/PD-L1 immunotherapy agents are eligible. Patients who have been treated with a PD-1/L1 agent in more than 1 line of therapy (as standard of care or in clinical trial) are not eligible. * Arm-specific eligibility criteria * Arm D: Anti-PD-1/PD-L1 treatment naïve patients only * Arm E \& F: Anti-PD-1/PD-L1 treatment experienced patients: Patients must have had refractory (Arm E=less than 24 weeks from first dose of anti-PD-1/PD-L1) or recurrent (Arm F=more than 24 weeks from first dose of anti-PD-1/PD-L1) disease during or after anti-PD-1 or anti-PD-L1 therapy and, in the opinion of the investigator, must be unlikely to benefit from nivolumab monotherapy. * Patients must have disease amenable to biopsy at the time of enrollment as biopsies are required for study participation. Exclusion Criteria: * Any active history of a known autoimmune disease. Subjects with vitiligo, type 1 diabetes mellitus, residual hypothyroidism requiring hormone replacement, or conditions not expected to recur in the absence of an external trigger are permitted to enroll. * Subjects with a history of interstitial lung disease that has required intubation in the past (i.e. such as Asthma or COPD). * Patients who have had chemotherapy or radiotherapy within 2 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 2 weeks earlier. * Patients who are receiving any other anticancer therapy. * Patients with uncontrolled brain metastases. Patients with brain metastases must have stable neurologic status following local therapy (surgery or radiation) for at least 2 weeks without the use of steroids or on stable or decreasing dose of \< 10mg daily prednisone (or equivalent), and must be without neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. Patients with a history of carcinomatous meningitis are not eligible. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to entinostat, azacitidine, or Nivolumab. * Known or suspected hypersensitivity to azacitidine or mannitol * Uncontrolled inter-current 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, azacitidine, and Nivolumab 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, azacitidine, or Nivolumab breastfeeding should be discontinued if the mother is treated on this protocol. * HIV-positive patients are excluded. (Patients cannot have known history of HIV. Testing for it at baseline is not required unless it is suspected they may have it). * Patients with active hepatitis B or hepatitis C are excluded. (Patients cannot have known history of hepatitis B or hepatitis C. Testing for it at baseline is not required unless it is suspected they may have it). * Patients with a condition requiring systemic treatment with either corticosteroids (\>10 mg daily prednisone equivalent) or other immunosuppressive medications within 14 days of randomization. Inhaled or topical steroids and adrenal replacement steroid doses \> 10 mg daily prednisone equivalent, are permitted in the absence of active autoimmune disease. * Patients with malabsorption in the small intestine or other conditions that would preclude administration of oral medication. * Prior therapy with DNA methyltransferase therapy or HDAC inhibitor therapy.