Inclusion Criteria:

          1. Dose Escalation Phase

             Arm 1 and Arm 2: Limited to subjects diagnosed with low grade CD-20 positive B-Cell
             NHL with at least one prior anticancer treatment.

          2. Dose Expansion Phase

             Arm 1 Cohort A: Limited to subjects with CD-20 positive CLL with at least one prior
             anticancer treatment.

             Arm 1 Cohort B: Limited to subjects with diagnosis of CD-20 positive NHL with at least
             one prior anticancer treatment.

             Arm 2 Cohort A: Limited to subjects with CD-20 positive CLL with at least one prior
             anticancer treatment.

             Arm 2 Cohort B: Limited to subjects with diagnosis of CD-20 positive NHL with at least
             one prior anticancer treatment.

          3. Disease status requirement:

               -  CLL subjects: symptomatic disease that mandate treatment;

               -  Indolent NHL subjects: symptomatic disease requiring treatment according to the
                  clinical judgment of the investigator;

               -  Other lymphoma subjects: disease requiring treatment according to the judgment of
                  the investigator.

          4. Eastern Cooperative Oncology Group (ECOG) Performance Status score of ≤2.

          5. Subject must have measurable disease using the disease-specific response criteria for
             NHL or CLL

          6. Age ≥ 18 years.

          7. Subject has recovered from all clinically significant toxicities related to prior
             antineoplastic therapies with the exception of alopecia and bone marrow and organ
             functions.

          8. Adequate organ system function ≤2 weeks prior to Day 1, defined as follows:

               -  Absolute neutrophil count (ANC) ≥1.0 x 109/L unless related to underlying CLL or
                  indolent NHL bone marrow involvement, and then ANC ≥500 x 109/L permitted.

               -  Platelets ≥100 x 109/L unless related to underlying CLL or indolent NHL bone
                  marrow involvement, and then platelets ≥75 x 109/L permitted.

               -  Subjects receiving IPI-145 plus rituximab with bone marrow involvement may enroll
                  with platelets ≥40 x 109/L.

               -  Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤1.5 x ULN
                  and total bilirubin ≤1.5 times the upper limit of normal (ULN) (except for
                  subjects with Gilbert's disease)

               -  Serum creatinine ≤1.5 x ULN

          9. Life expectancy of ≥12 weeks.

         10. Women of child-bearing potential (WCBP) must have a negative serum or urine pregnancy
             test.

         11. Ability to understand the nature of this study and give written informed consent.

        Exclusion Criteria:

          1. Prior allogeneic hematopoietic stem cell transplant (HSCT).

          2. Prior autologous transplant or radioimmunotherapy ≤6 months prior to the first dose of
             trial treatment.

          3. Subject has a high grade lymphoma such as Burkitt's, lymphoblastic or small
             non-cleaved cell lymphomas. Subjects with intermediate grade lymphoma (such as diffuse
             large B-cell lymphoma) are eligible.

          4. Subjects with diffuse B-cell lymphoma must either not be eligible for autologous bone
             marrow transplant (BMT) or relapsed after autologous BMT.

          5. More than three previous cytotoxic chemotherapy regimens for subjects treated on the
             arm containing bendamustine.

          6. Subjects who have had a severe allergic or anaphylactic reaction to any humanized or
             murine monoclonal antibodies.

          7. Chemotherapy, cancer immunosuppressive therapy, growth factors (except
             erythropoietin), radiation therapy (other than whole brain irradiation [WBI]) surgery
             or ablative therapy or investigational drugs/devices ≤28 days before first dose of
             trial treatment.

          8. Subjects receiving high doses of corticosteroids must have been tapered to a stable
             dose at least 7 days before the first dose of trial treatment.

          9. Tyrosine kinase inhibitor within 7 days prior to the first dose of trial treatment.

         10. Subjects with overt leptomeningeal leukemia or central nervous system (CNS) lymphoma.
             Subjects must be free of CNS disease for a minimum of 2 months. Subjects with symptoms
             of CNS disease must have a negative diagnostic lumbar puncture prior to study
             enrollment.

         11. Subjects with a history of stroke, unstable angina, myocardial infarction, or
             ventricular arrhythmia requiring medication or mechanical control within the last 6
             months.

         12. Baseline QTcF >480 ms. Note: This criterion does not apply to subjects with a left
             bundle branch block.

         13. Subjects who have had a venous thromboembolic event requiring anticoagulation and who
             meet any of the following criteria:

               -  Have been on a stable dose of anticoagulation for <1 month.

               -  Have had a Grade 2, 3 or 4 hemorrhages in the last 30 days.

               -  Are experiencing continued symptoms for their venous thromboembolic event.

         14. Subjects with a history of liver disease as a result of alcohol abuse, chronic
             hepatitis, or other chronic liver disease (other than metastatic disease to the
             liver).

         15. Subjects with positive HBsAg, HBcAb or HCV are excluded.

         16. Subjects with a history of tuberculosis within the preceding two years.

         17. Prior surgery affecting drug absorption or any gastrointestinal dysfunction that could
             alter drug absorption.

         18. Subjects with a known hypersensitivity to bendamustine or rituximab.

         19. Presence of active infection within 72 hours of treatment. Subjects 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.

         20. Known diagnosis of human immunodeficiency virus (HIV).

         21. Concurrent administration of medications or foods that are strong or moderate
             inhibitors or inducers of CYP3A.

         22. Women who are pregnant or lactating.

         23. Psychological, familial, sociological, or geographical conditions that do not permit
             compliance with the protocol.

         24. Concurrent condition that in the investigator's opinion would jeopardize compliance
             with the protocol or would impart excessive risk associated with study participation
             that would make it inappropriate for the subject to be enrolled.

         25. Inability or unwillingness to comply with study and/or follow-up procedures outlined
             in the protocol.