Brief Summary: This phase I/II trial tests the safety, side effects, and best dose of entinostat and ZEN003694 in treating patients with solid tumors or lymphoma that has spread to other places in the body (advanced) or does not respond to treatment (refractory). Entinostat may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. It is in a class of drugs called histone deacetylase (HDAC) inhibitor. ZEN003694 is an inhibitor of a family of proteins called the bromodomain and extra-terminal (BET). ZEN003694 may prevent the growth of tumor cells that produce high levels of BET protein. This trial aims to test the safety of combination therapy with entinostat and ZEN003694 in treating patients with advanced or refractory solid tumors or lymphoma.

Detailed Description: PRIMARY OBJECTIVES: I. To determine the maximum tolerated dose (MTD) of BET bromodomain inhibitor ZEN-3694 (ZEN003694) and entinostat in combination in patients with advanced and refractory solid tumors and lymphomas based on dose limiting toxicities (DLTs) of the combination of ZEN003694 and entinostat. (Phase I) II. To determine the overall response rate (ORR) of ZEN003694 and entinostat in advanced/progressive pancreatic cancer. (Phase II) SECONDARY OBJECTIVES: I. To describe the safety profile of ZEN003694 and entinostat in advanced and refractory solid tumors and lymphomas. (Phase I) II. To determine the progression-free survival (PFS), duration of response (DOR), and overall survival (OS) of ZEN003694 and entinostat in this patient population. (Phase I) III. To describe the safety profile of ZEN003694 and entinostat in advanced/progressive pancreatic cancer. (Phase II) IV. To determine the progression-free survival (PFS), duration of response (DOR), and overall survival (OS) of ZEN003694 and entinostat in this patient population. (Phase II) V. To assess the effect of ZEN003694 and entinostat therapy on apoptosis, as measured by an apoptosis multiplex immunoassay. (Phase I \& II) EXPLORATORY OBJECTIVES: I. To assess the effect of ZEN003694 and entinostat therapy on c-MYC and YAP1 as measured by apoptosis immunofluorescence assay. II. To assess the effect of ZEN003694 and entinostat therapy on c-MYC and YAP1 as measured by ribonucleic acid (RNA) and protein expression. III. To assess the effect of ZEN003694 and entinostat therapy on tumor burden and gene expression patterns as measured by whole exome sequencing (WES) and RNA sequencing (RNASeq) on circulating tumor deoxyribonucleic acid (DNA) (ctDNA) specimens. OUTLINE: This is a phase I, dose-escalation study of ZEN003694 in combination with entinostat followed by a phase II study. PHASE I RUN-IN PERIOD: Patients receive ZEN003694 orally (PO) once daily (QD) during days -14 to 1. Patients also undergo core needle biopsy within 30 days prior to starting therapy. PHASE II RUN-IN PERIOD: Patients receive ZEN003694 PO QD or entinostat PO once per week (QW) during days -14 to 1 based on the order to which they are enrolled to the study (e.g. every other patient starts by taking ZEN003694 alone for 14 days). Patients also undergo core needle biopsy within 30 days prior to starting therapy. PHASE I \& II COMBINATION TREATMENT: Patients receive entinostat PO QW on days 1, 8, 15, and 22, and ZEN003694 PO QD on days 1-28. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. Patients also undergo core needle biopsy on day 1 of cycle 1, and on day 1 of cycle 14. After completion of study treatment, patients are followed for 30 days.