A Study Evaluating the Safety and Pharmacokinetics of ABT-199 in Combination With Bendamustine/Rituximab (BR) in Subjects With Relapsed or Refractory Non-Hodgkin's Lymphoma

* Subject must have histologically documented diagnosis of non-Hodgkin's lymphoma as defined by a B-cell neoplasm in the World Health Organization classification scheme except as noted in exclusion criteria. * Subject (non-diffuse large B-cell lymphoma) must have relapsed or refractory non-Hodgkin's lymphoma, and require treatment in the opinion of the investigator. * Subject with diffuse large B-cell lymphoma must have relapsed diffuse large B-cell lymphoma or must have progressed after salvage therapy (with or without standard chemotherapy) for diffuse large B-cell lymphoma. The subject must have received first line therapy with Rituximab-Cyclophosphamide, Hydroxydaunomycin, Vincristine (Oncovin), Prednisone (R-CHOP) \[or a similar standard rituximab-containing front-line chemoimmunotherapy regimen including, but not limited to Etoposide, Prednisone, Vincristine (Oncovin), Cyclophosphamide, Doxorubicin (Hydrochloride) + Rituximab (EPOCH + R); Rituximab, Cyclophosphamide, Etoposide, Procarbazine, Prednisone (RCEPP); Rituximab, Cyclophosphamide, Mitoxantrone (Novantrone), Vincristine (Oncovin), Prednisone (RCNOP); Dose-adjusted-Etoposide, Prednisone, Vincristine(Oncovin), Cyclophosphamide, Doxorubicin (Hydrocloride) (DA-EPOCH); and Rituximab, Cyclophosphamide, Etoposide, Vincristine (Oncovin), Prednisone (RCEOP)\]. * Subject must have adequate coagulation, renal, and hepatic function, per laboratory reference range at Screening.

* Subject has been diagnosed with Post-Transplant Lymphoproliferative Disease, Burkitt's lymphoma, Burkitt-like lymphoma, lymphoblastic lymphoma/leukemia, chronic lymphocytic leukemia, small lymphocytic lymphoma or mantle cell lymphoma (MCL). * Subject has refractory diffuse large B-cell lymphoma, defined as meeting any of the following criteria: * Subject progressed during or within 3 months of completion of a planned course of first-line therapy with Rituximab-Cyclophosphamide, Hydroxydaunomycin, Vincristine (Oncovin), Prednisone (R-CHOP) or an equivalent regimen; * Subject had no response (i.e., stable disease only) to first-line therapy with R-Cyclophosphamide, Hydroxydaunomycin, Vincristine (Oncovin), Prednisone (R-CHOP) or an equivalent regimen; * Subject progressed during or within 2 months of completion of their last planned course of salvage therapy with chemotherapy (with or without rituximab, may include autologous stem cell transplant). * Subject has tested positive for human immunodeficiency virus (HIV). * Subject has a cardiovascular disability status of New York Heart Association Class greater or equal to 2. Class 2 is defined as cardiac disease in which patients are comfortable at rest but ordinary physical activity, results in fatigue, palpitations, dyspnea or anginal pain. * Subject has a significant history of renal, neurologic, psychiatric, endocrinologic, metabolic, immunologic, or hepatic disease that in the opinion of the Investigator would adversely affect his/her participating in this study.