I. To assess safety, characterize toxicities, and determine the maximum tolerated dose of 5-AZA (azacitidine) with a fixed-dose of entinostat in patients with recurrent advanced non-small cell lung cancer (NSCLC). (Phase I) II. To determine the objective response rate of 5-AZA and entinostat in patients with recurrent NSCLC. (Phase II)