CPI-613, Bendamustine Hydrochloride, and Rituximab in Treating Patients With Relapsed or Refractory B-Cell Non-Hodgkin Lymphoma

Inclusion Criteria: * Histologically and cytologically confirmed B-cell NHL that has relapsed from, or is refractory to, all standard therapies (including autologous transplantation) known to provide clinical benefit, but have not been treated with bendamustine for their lymphoma * Must have measurable disease (e.g., a tumor mass \> 1 cm) * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Expected survival \> 3 months * Women of child-bearing potential (i.e., women who are pre-menopausal or not surgically sterile) must use accepted contraceptive methods (abstinence, intrauterine device \[IUD\], oral contraceptive or double barrier device) during the study, and must have a negative serum or urine pregnancy test within 1 week prior to treatment initiation * Fertile men must practice effective contraceptive methods during the study, unless documentation of infertility exists * At least 2 weeks must have elapsed from any prior surgery * Aspartate aminotransferase (AST/serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT/serum glutamate pyruvate transaminase \[SGPT\]) =\< 3 x upper normal limit (UNL) (=\< 5 x UNL if liver metastases present) * Bilirubin =\< 1.5 x UNL * Serum creatinine =\< 1.5 mg/dL or 133 umol/L * "International normalized ratio" or INR must be =\< 1.5 * No evidence of active infection and no serious infection within the past month * Mentally competent, ability to understand and willingness to sign the informed consent form Exclusion Criteria: * Known cerebral metastases, central nervous system (CNS) or epidural tumor * Having "currently active" second malignancy unrelated to Hodgkin lymphoma (HL) or NHL, unless they have completed anti-cancer therapy, are in complete response and are considered by their physicians to be at less than 30% risk of relapse * Patients receiving any other standard or investigational treatment for their cancer, or any other investigational agent for any indication, within the past 2 weeks prior to initiation of treatment with study drugs * Serious medical illness that would potentially increase patients' risk for toxicity * Any active uncontrolled bleeding, and any patients with a bleeding diathesis (e.g., active peptic ulcer disease) * History of abdominal fistula or gastrointestinal perforation =\< 6 months prior to treatment with study drugs * Pregnant women, or women of child-bearing potential not using reliable means of contraception * Lactating females * Fertile men unwilling to practice contraceptive methods during the study period * Any condition or abnormality which may, in the opinion of the investigator, compromise the safety of patients * Unwilling or unable to follow protocol requirements * Active heart disease including but not limited to symptomatic congestive heart failure, symptomatic coronary artery disease, symptomatic angina pectoris, symptomatic myocardial infarction or symptomatic congestive heart failure * Patients with a history of myocardial infarction that is \< 3 months prior to registration * Evidence of active infection, or serious infection within the past month * Patients with known human immunodeficiency virus (HIV) infection, hepatitis B, or hepatitis C * Patients who have received cancer immunotherapy of any type within the past 2 weeks prior to initiation of CPI-613 treatment * Requirement for immediate palliative treatment of any kind including surgery