Duvelisib and Venetoclax in Relapsed or Refractory CLL or SLL or RS

Inclusion Criteria: * Must have a confirmed diagnosis of chronic lymphocytic leukemia or small lymphocytic lymphoma requiring therapy, as per IW-CLL 2008 criteria OR Biopsy proven transformation to diffuse large B cell lymphoma (DLBCL), consistent with Richter's Syndrome * Disease that has progressed during or relapsed after at least one previous CLL/SLL therapy - If Richter's Syndrome, this criterion is not applicable * Age greater to or equal to 18 years * ECOG performance status ≤2 (Karnofsky ≥60%) * Patients must meet the following hematologic criteria at screening, unless they have significant bone marrow involvement of CLL confirmed on biopsy: * Absolute neutrophil count ≥500 cells/mm3 (0.5 x 109/L). Growth factor is allowed in order to achieve this * Platelet count ≥25,000 cells/mm3 (25 x 109/L) independent of transfusion within 7 days of screening * Adequate hepatic function defined as: --Serum aspartate transaminase (AST) and alanine transaminase (ALT) ≤ 3.0 x upper limit of normal (ULN), bilirubin ≤1.5 x ULN (unless bilirubin rise is due to Gilbert's syndrome or of non-hepatic origin * Adequate renal function as defined as: --Serum creatinine ≤1.5 times the upper limit of normal or creatinine clearance ≥ 50 mL/min using a 24-hour urine collection * Women of child-bearing potential and men must agree to use adequate contraception (hormonal, barrier method or abstinence) prior to study entry and for the duration of study participation * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Previous treatment with venetoclax or duvelisib * Patients receiving cancer therapy (i.e., chemotherapy, radiation therapy, immunotherapy, biologic therapy, surgery within 2 weeks of Cycle 1/Day 1 with the following exceptions: * For patients on targeted therapies, a washout of least five half lives is required * Patients who experience clinical deterioration may start therapy after a shorter washout period with prior approval by the PI * Corticosteroid therapy (prednisone or equivalent \<20 mg daily) is allowed * Confirmed central nervous system involvement * Allogeneic hematologic stem cell transplant within 6 months of starting study treatment or active graft vs. host disease (GVHD) requiring treatment or prophylaxis * History of active malignancy requiring therapy with the exception of hormonal therapy * Any active systemic infection requiring IV antibiotics or uncontrolled, active infections * Known history of human immunodeficiency virus (HIV), hepatitis C virus (HCV), or hepatitis B virus (HBV) * Major surgery within 4 weeks of first dose of study drug * Currently active gastrointestinal disease, including colitis, inflammatory bowel disease and diarrhea requiring therapy * Currently active, clinically significant cardiovascular disease, such as uncontrolled arrhythmia or Class 3 or 4 congestive heart failure as defined by the New York Heart Association Functional Classification; or a history of myocardial infarction, unstable angina, or acute coronary syndrome within 6 months prior to randomization * Any life-threatening illness, medical condition, or organ system dysfunction that, in the investigator's opinion, could compromise the subject's safety or put the study outcomes at undue risk * Use of Coumadin for anticoagulation (other anticoagulants permitted) * Lactating or pregnant * Concurrent administration of medications or foods that are strong inhibitors or inducers of CYP3A (see Appendix D) . The concomitant use of drugs or foods that are strong or moderate inhibitors or inducers of CYP3A are not allowed beginning 1 week prior to the first dose of duvelisib. * Patients with ongoing use of prophylactic antibiotics are eligible as long as there is no evidence of active infection and the antibiotic is not included on the list of prohibited medications * Unable to swallow capsules or malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel, symptomatic inflammatory bowel disease or ulcerative colitis, or partial or complete bowel obstruction resulting in malabsorption or chronic diarrhea * Active abuse of alcohol * History of chronic liver disease or veno-occlusive disease/sinusoidal obstruction syndrome * History or concurrent condition of interstitial lung disease of any severity and/or severely impaired lung function * Known hypersensitivity to duvelisib and/or its excipients * History of tuberculosis treatment within the 2 years prior to initiation of therapy