A Study of Duvelisib and Venetoclax in Subjects With Relapsed or Refractory Chronic Lymphocytic Leukemia, Small Lymphocytic Lymphoma, or Indolent or Aggressive Non-Hodgkin Lymphoma, Who Have Not Previously Received a Bcl-2 or PI3K Inhibitor

Inclusion Criteria: - Subject must have either • Relapsed or refractory Chronic Lymphocytic Leukemia/Small Lymphocytic Lymphoma (for Waves 2 or 3) * Subject has evaluable disease and requires treatment in the opinion of the investigator. * Subject must have relapsed following or be refractory to ≥ 1 standard treatments such as fludarabine based regimens (F, FC, FR, FCR), alkylator (chlorambucil, bendamustine) based regimens, or Bruton's Tyrosine Kinase inhibitor (Ibrutinib). Or • Relapsed or refractory indolent Non-Hodgkin Lymphoma or aggressive Non-Hodgkin Lymphoma (for Waves 1, 2, or 3, unless otherwise indicated) * Subject must have histologically documented diagnosis of a Follicular Lymphoma or Marginal Zone Lymphoma. * Subject must have histologically documented diagnosis of a Diffuse Large B-cell Lymphoma (excluding Richter's Transformation), Non-cutaneous T-Cell Lymphoma, or Mantle Cell Lymphoma (MCL) (MCL Wave 3 only) * Subject has evaluable disease and requires treatment in the opinion of the investigator. * Subject must have relapsed following or be refractory to ≥ 1 standard treatments such as R-CHOP, R-CVP, bendamustine, lenalidomide-rituximab, or fludarabine-based regimens. * Subject has an Eastern Cooperative Oncology Group (ECOG) performance score of less than or equal to 2. * Subject must have adequate bone marrow independent of growth factor support per local laboratory reference range at Screening. * Subject must have adequate coagulation, renal, and hepatic function, per laboratory reference range at Screening. * NHL subjects who have a history of an autologous stem cell transplant (e.g., bone marrow) must be \> 6 months post-transplant (prior to the first dose of study drug) and must not require any growth factor support. Exclusion Criteria: * Subject has been previously treated with a Bcl-2 or PI3K inhibitor. * Subject is a candidate to receive another second-line therapy approved for usage by the local Health Authority. * Subject is appropriate for a stem cell transplant or has undergone an allogeneic stem cell transplant. * Subject has received any of the following within 14 days or 5 drug half-lives (whichever is shortest) prior to the first dose of duvelisib or venetoclax, or has not recovered to less than Grade 2 clinically significant adverse effect(s)/toxicity(s) of the previous therapy: * Any anti-cancer therapy including chemotherapy or radiotherapy; * Investigational therapy, including targeted small molecule agents. * Subject has received biologic agents (e.g., monoclonal antibodies) for anti-neoplastic treatment within 30 days prior to first dose of duvelisib or venetoclax. * Subject has received live or live attenuated vaccines within 6 weeks prior to first dose of duvelisib or venetoclax. * Subject has received the following within 7 days prior to the first dose of duvelisib or venetoclax: * Steroid therapy for anti-neoplastic treatment; * Strong and Moderate CYP3A inhibitors; * Strong and Moderate CYP3A inducers; * Chronic immunosuppressants, other than corticosteroids given at daily dose \< 20 mg prednisone equivalent for ITP or AIHA.