Inclusion Criteria:  Patients must have advanced or refractory solid tumor or lymphoma (all B cell lymphomas and T cell lymphomas other than natural killer [NK]-cell lymphoma) For patients in Phase 2: Patients must have locally advanced, unresectable OR metastatic pancreatic cancer refractory to standard therapy Patients must have measurable disease based on Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria Patients should have received previous therapy 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 >= 150,000/mcL (measured within 14 days prior to administration of study treatment) Total bilirubin =< 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) Serum bilirubin =< 1.5 x institutional ULN (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 with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be 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 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  Exclusion Criteria:  Patients who have had any anti-cancer therapy within 14 days (or 5 half-lives, whichever is longer) prior to the first dose of the investigational products Patients who have received radiation therapy within 21 days prior to the first dose of the investigational products Patients who have a diagnosis of NK cell lymphoma Patients who have not recovered from adverse events due to prior anti-cancer therapy (i.e., have residual toxicities > grade 1) with the exception of alopecia, or stable chronic grade 2 toxicities that do not overlap with presumed toxicities of entinostat or ZEN003694 Patients who are receiving any other investigational agents Patients with known untreated or symptomatic brain or leptomeningeal metastases are excluded. Patients with previously treated CNS metastasis may be included provided that they have stable CNS disease for at least 4 weeks (confirmed by imaging) without symptoms and are off corticosteroids (above physiologic dose) for that indication Patients with significant malabsorption or nausea and vomiting that would interfere with oral therapies Patients with bleeding diathesis or clinically significant bleeding within the prior 6 months History of allergic reactions attributed to compounds of similar chemical or biologic composition to entinostat (e.g. medications that have a benzamide structure (tiapride, remoxipride, clebopride) or ZEN003694 Patients receiving any medications or substances that are strong inhibitors or strong inducers of CYP3A4 or substrates of CYP1A2 with narrow therapeutic windows are ineligible. Strong inhibitors or inducers of CYP3A4 and substrates of CYP1A2 must be discontinued at least 7 days prior to the first dose of ZEN003694. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently updated medical reference. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product Patients with uncontrolled intercurrent illness Patients with psychiatric illness/social situations that would limit compliance with study requirements Pregnant women are excluded from this study because entinostat is an HDACi and ZEN003694 is a BETi 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 or ZEN003694, breastfeeding should be discontinued throughout the treatment period and for at least 28 days following the last dose of study treatment if the mother is treated with entinostat or ZEN003694  Patients with either of the following cardiac criteria:  Patients with a corrected QT interval calculated by the Fridericia formula (QTcF) > 450 msec by electrocardiogram (ECG). Concomitant use of any agent known to cause corrected QT interval (QTc) prolongation. Clinically significant conduction abnormalities or arrhythmias. Presence of a cardiac pacemaker or defibrillator with a paced ventricular rhythm limiting ECG analysis. History or evidence of current >= Class II congestive heart failure as defined by New York Heart Association (NYHA). History of acute coronary syndromes (including unstable angina and myocardial infarction), coronary angioplasty, or stenting within the past 6 months. Subjects with a history of stent placement requiring ongoing antithrombotic therapy (e.g. clopidogrel, prasugrel) will not be permitted to enroll. Clinically significant cardiomegaly, ventricular hypertrophy, or cardiomyopathy Use of oral Factor Xa inhibitors (i.e., rivaroxaban, apixaban, betrixaban, edoxaban otamixaban, letaxaban, eribaxaban) and Factor IIa inhibitors (i.e., dabigatran). Low molecular weight heparin is allowed Patients with radiation to > 25% of the bone marrow Patients who have had a bone-targeted radionuclide within 6 weeks of the first dose of ZEN003694 Patients who have previously received ZEN003694 or who have been treated with an HDAC inhibitor or investigational BET inhibitor Major surgery other than diagnostic surgery, dental surgery or stenting within 4 weeks prior to the first dose of ZEN003694