IIT CTI Bendamustine, Rituximab, Pixantrone in Relapsed/Refractory B Cell Non-Hodgkin's Lymphoma

Inclusion Criteria: 1. Part I: Subjects must have relapsed or refractory B cell NHL; 2. Part II: Subjects must have relapsed or refractory aggressive B cell NHL including follicular lymphoma (FL) grade 3, Diffuse Large B Cell Lymphoma (DLBCL), transformed NHL, mantle cell lymphoma (MCL), or other aggressive B cell NHL histology as per the WHO 2008 criteria; 3. Refractory disease (defined as persistence of evaluable disease after therapy) or relapsed disease following at least one prior treatment regimen that should include autologous stem cell transplant unless a patient was not eligible or refused prior transplant; 4. Age ≥ 18 years old; 5. Eastern Cooperative Oncology Group (ECOG) performance status of ≤2; 6. Subjects must have measurable or evaluable disease based on physical exam and/or radiographs (CT, MRI, PET) or bone marrow involvement; 7. Female subject is either post-menopausal or surgically sterilized; 8. Laboratory Values: * Absolute neutrophil count (ANC) ≥ 1.5 x 10\^9/L; lower levels accepted if due to marrow involvement by lymphoma * Platelets ≥ 75,000/mcl; lower levels accepted if due to marrow involvement by lymphoma * Total bilirubin ≤ 1.5 X institutional upper limit of normal; ≤ 3.0 ULN accepted in subjects with Gilbert's Syndrome * AST/ALT ≤ 1.5 X institutional upper limit of normal. Subjects with known liver involvement by lymphoma: AST/ALT ≤ 2 X institutional upper limit of normal * Serum creatinine \< 1.5 X institutional upper limit of normal 9. Ability to provide written informed consent obtained prior to participation in the study and any related procedures being performed Exclusion Criteria: 1. No chemotherapy, radiation, biologics or immunotherapy within 2 weeks prior to registration (6 weeks if last received BCNU or mitomycin C). 2. No radioimmunotherapy within 2 months prior to registration. 3. Subjects receiving chronic, systemic treatment with corticosteroids equivalent to \> 20mg of prednisone per day. Subjects receiving replacement for adrenal insufficiency will be allowed on the study. Topical or inhaled corticosteroids are allowed. 4. Subjects with a history of another primary malignancy ≤ 3 years ago, with the exception of inactive basal, squamous cell carcinoma of the skin or superficial melanoma only requiring excision, prostate cancer with a PSA that has not increased for at least 3 months, carcinoma in situ of the cervix. 5. Major surgery ≤ 4 weeks prior to registration. Minor surgery ≤ 2 weeks prior to registration. Insertion of a vascular access device is not considered major or minor surgery. Subjects must have recovered from all surgery related toxicities to ≤ grade 1 or to baseline if subject started with \> grade 1 toxicity, not otherwise violating the above inclusion criteria. 6. Subjects who have received investigational drugs ≤ 4 weeks prior to registration. 7. Impaired Cardiac Function: * QTc \> 480 on screening ECG. * Previous history of angina pectoris or acute MI within 6 months * Congestive heart failure (New York Heart Association functional classification III-IV) or baseline MUGA/ECHO shows estimated LVEF \< 45% * Any history of torsade de pointes, ventricular fibrillation, uncontrolled ventricular tachycardia, or uncontrolled atrial fibrillation. 8. Female patients who are pregnant or breastfeeding 9. Patients with history of untreated hepatitis B or who are known carriers of hepatitis B will be excluded from this trial. All subjects will be screened prior to study entry. 10. Concurrent use of other anti-cancer agents or anti-cancer treatments.