• Patients must have a) advanced or refractory solid tumor or b) lymphoma (all B cell lymphomas and T cell lymphomas other than natural killer \[NK\]-cell lymphoma) and must meet standard requirements for treatment

• For patients in Phase 2: Patients must have locally advanced, unresectable OR metastatic pancreatic cancer refractory to standard therapy

• For patients with solid tumors, they must have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria. For patients with lymphoma, they must have measurable disease based on Response Evaluation Criteria in Lymphoma (RECIL) criteria, or Lugano Classification criteria

• For patients with solid tumors, they must have received at least one standard of care regimen for metastatic disease. For patients with lymphoma, they should have received at least two previous therapies with at least one combination chemotherapy regimen for metastatic disease

• Patients with lymphoma must have exhausted or refused potential curative therapy prior to enrolling

• Age \>= 18 years. Because no dosing or adverse event data are currently available on the use of ZEN003694, alone or in combination with entinostat, in patients \< 18 years of age, children are excluded from this study

• Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 (Karnofsky \>= 60%)

• Hemoglobin \>= 9.0 g/dL (measured within 14 days prior to administration of study treatment)

• Absolute neutrophil count (ANC) \>= 1,500/mcL (measured within 14 days prior to administration of study treatment)

• Platelets \>= 100,000/mcL (measured within 14 days prior to administration of study treatment)

• Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) (measured within 14 days prior to administration of study treatment)

• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2.5 x institutional ULN (measured within 14 days prior to administration of study treatment)

• Serum creatinine clearance \> 50 mL/min (measured within 14 days prior to administration of study treatment)

• Glomerular filtration rate (GFR) \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal (measured within 14 days prior to administration of study treatment)

• Prothrombin time (PT)/international normalized ratio (INR) and partial thromboplastin time (PTT) test \< 1.5 x ULN (measured within 14 days prior to administration of study treatment)

• Troponin =\< ULN (measured within 14 days prior to administration of study treatment)

• Albumin \> 2.5 g/dL (measured within 14 days prior to administration of study treatment)

• Patients with treated brain metastases are eligible if follow-up brain imaging at least 4 weeks after central nervous system (CNS)-directed therapy shows no evidence of progression

• Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial

• Patients should be New York Heart Association Functional Classification of class 2B or better

• Patients must be able to swallow and retain orally administered medication

• Women of childbearing potential must have a negative pregnancy test within 7 days of starting treatment

• The effects of entinostat and ZEN003694 on the developing human fetus are unknown. For this reason and because histone deacetylase inhibitor (HDACi) and BET inhibitor (BETi) agents are known to be teratogenic, women of child-bearing potential and their male partner must agree to use contraception from the time of the screening pregnancy test, continuing for the duration of study participation, and for 3 months after completing the study treatment

• Patients must have tumors determined to be easily accessible for biopsy and must be willing to have serial biopsies. Tumor biopsies will be performed on the most accessible biopsiable site of disease. All possible precautions to avoid complications will be taken, including discussions in multidisciplinary meetings, if needed. If a biopsy cannot be performed safely (e.g. there is no safely accessible biopsiable tumour tissue) or biopsy does not yield sufficient tissue for analysis, participation is still allowed

• Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity who have a legally-authorized representative (LAR) and/or family member available will also be eligible

• Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load