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

This research study is assessing a new drug, duvelisib, in combination with a drug that is already FDA approved, venetoclax, as a possible treatment for participants with CLL or those with Richter's Syndrome

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 \