A Study of ZEN003694 in People With Squamous Cell Lung Cancer

Inclusion Criteria: * Histologically-confirmed squamous cell lung cancer * Recurrent or metastatic disease * Patients with previously treated asymptomatic brain metastases requiring no more than 10mg prednisone (or equivalent) are allowed. Patients with asymptomatic brain metastases ≤ 1cm not requiring more than 10mg prednisone (or equivalent) are allowed. * Received prior first-line therapy: platinum-based chemotherapy and immunotherapy, given either concurrently or sequentially * Eastern Cooperative Oncology Group (ECOG) PS 0-2 * Evidence of NSD3 gain or amplification by NGS, including but not limited to evidence of 8p11 gain or amplification as determined by MSK IMPACT or MSK ACCESS, or a commercially available molecular assay that is FDA authorized. Note: ctDNA testing, including but not limited to MSK ACCESS and Guardant and Foundation * Adequate laboratory parameters at Screening including: * Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L * Platelet count ≥ 100,000/mm\^3 * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) ≤ 2.0 ULN (≤ 5 x ULN if liver metastases are present) * Total bilirubin ≤ 1.25 x ULN * Calculated or measured eGFR ≥ 40 ml/min or serum creatinine ≤ 1.5 x ULN * Prothrombin time (PT), international normalized ratio (INR) and partial thromboplastin time (PTT) \< 1.5 x ULN * Ability to swallow capsules * Use of corticosteroids is allowed up to a daily dose of 10 mg prednisone or equivalent provided that the dose has been stable for at least 2 weeks prior to the start of ZEN003694 dosing and will remain stable during ZEN003694 treatment. * Females or males age ≥ 18 years (at time of signing informed consent) * Female subjects may be enrolled if they are not of childbearing potential, permanently sterile or who are post-menopausal defined as no menses for at least 1 year without an alternative medical cause and FSH levels in the post-menopausal range. Female subjects of childbearing potential may be enrolled if they consistently and correctly use a highly effective form of contraception. Highly effective forms of contraception include: combined (estrogen and progestogen hormonal contraceptives (oral, intravaginal, transdermal) associated with inhibition of ovulation; progestogen-only hormonal contraception (oral, injectable, implantable) associated with inhibition of ovulation; intrauterine device (IUD); intrauterine hormone-releasing system (IUS); bilateral tubal occlusion; vasectomized partner; sexual abstinence. Female subjects should not donate eggs from the time point of study drug administration until at least 7 months thereafter. * Males with partners of childbearing potential may be enrolled if they use a condom when having sex with a pregnant woman or with a non-pregnant female of childbearing potential from 21 days before the first dose of study drug through 4 months after the last dose of study drug, and males should not donate sperm from the time point of study drug administration until at least 4 months thereafter. Contraception should be considered for a non-pregnant female partner of childbearing potential * Females of childbearing potential must have a negative serum or urine pregnancy test before the first dose of study drugs and must agree to pregnancy tests during the study. * Females may not be breast-feeding at the first dose of study drugs, during study participation or through 7 months after the last dose of study drugs Exclusion Criteria: * Have previously received an investigational BET inhibitor * Have received prior systemic anti-cancer therapy or investigational therapy within 2 weeks or five half-lives, whichever is shorter, prior to the first dose of study drug * Radiation therapy within 2 weeks of first dose of study drug * Currently receiving medications known to be strong inducers or inhibitors of CYP3A4 and substrates of CYP1A2 with a narrow therapeutic window. Strong inducers and inhibitors of CYP3A4 and CYP1A2 substrates with narrow therapeutic ranges must be discontinued at least 7 days prior to the first administration of study drug. * Left ventricular ejection fraction less than the lower of 50% or the lower limit of institution's normal range * QTcF interval \> 470 msec * Known impaired cardiac function or clinically significant cardiac disease such as uncontrolled supraventricular arrhythmia, ventricular arrhythmia requiring therapy, or uncontrolled congestive heart failure (New York Heart Association functional class III or IV) * Myocardial infarction or unstable angina within 6 months prior to the first administration of study drug * Other clinically significant co-morbidities, such as uncontrolled pulmonary disease, active CNS disease, active, uncontrolled bacterial, viral, or fungal infection(s) requiring systemic therapy, or any other condition that could compromise safety or the patient's participation in the study * Other known active cancer requiring therapy at time of study entry * Historically positive (screening tests not required) for human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus (HCV) or with active infections. HBV positivity defined by positive hepatitis B surface antigen (HBsAg). HCV positivity defined as positive HCV viral load. * Major surgery other than diagnostic surgery, dental surgery or stenting within 4 weeks prior to the first administration of study drug * History of congenital or other deficiency in platelet function, or any known inherent or acquired coagulopathy, including current anticoagulation therapy (except for low-dose warfarin for port patency) * Current or anticipated use within 7 days prior to the first administration of study drug, or during the study, of strong P-gp inhibitors. * 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. Note: except for subjects on anticoagulant therapy who must have PT-INR within therapeutic range as deemed appropriate by the Investigator.