Rituxan/Bendamustine/PCI-32765 in Relapsed DLBCL, MCL, or Indolent Non-Hodgkin's Lymphoma

Inclusion Criteria:

* Histologically confirmed B-cell NHL of the following subtypes: follicular, marginal zone (nodal, splenic, or extranodal), Waldenstrom's macroglobulinemia, diffuse large B-cell (DLCL) or mantle cell lymphoma (MCL) according to 2008 World Health Organization (WHO) criteria that is relapsed or refractory after at least 1 prior therapy

  * Patients with DLCL must be relapsed or refractory after previous autologous stem cell transplant unless transplant is contraindicated
  * Patients with MCL, follicular lymphoma (FL), marginal zone lymphoma, or Waldenstrom's macroglobulinemia are eligible after \>= 1 prior therapies; however, patients with MCL who are not eligible for stem cell transplant (due to age or other co-morbidities) or refuse up-front stem cell transplantation may receive study treatment as their first-line therapy
* Body weight \>= 40 kg
* Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2
* Agreement to use contraception during the study and for 30 days after the last dose of study drug if sexually active and able to bear children
* Willing and able to participate in all required evaluations and procedures in this study protocol including swallowing capsules without difficulty
* Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information (in accordance with national and local patient privacy regulations)

Exclusion Criteria:

* Prior malignancy, except for adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, or other cancer from which the patient has been disease free for at least 2 years or which will not limit survival to \< 2 years (Note: these cases must be discussed with the Principal Investigator)
* A life-threatening illness, medical condition or organ system dysfunction which, in the investigator's opinion, could compromise the patient's safety, interfere with the absorption or metabolism of PCI-32765 PO, or put the study outcomes at undue risk
* Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, congestive heart failure, or myocardial infarction within 6 months of screening, or any Class 3 or 4 cardiac disease as defined by the New York Heart Association Functional Classification
* Malabsorption syndrome, disease significantly affecting gastrointestinal function, or resection of the stomach or small bowel or ulcerative colitis, symptomatic inflammatory bowel disease, or partial or complete bowel obstruction
* Any immunotherapy, chemotherapy, radiotherapy, or experimental therapy within 3 weeks before first dose of study drug (corticosteroids for disease-related symptoms allowed but require 1-week washout before study drug administration)
* Use of medications known to prolong QTc interval or that may be associated with Torsades de Pointes are prohibited within 7 days of starting study drug and during treatment
* Central nervous system (CNS) involvement by lymphoma
* Grade \>= 2 toxicity (other than alopecia) related to prior anticancer therapy including radiation
* Known history of human immunodeficiency virus (HIV), active infection with hepatitis C virus (HCV) or hepatitis B virus (HBV surface antigen positive), carriers of HBV (surface antigen and surface antibody negative, but HBV core antibody positive), or any uncontrolled active systemic infection
* Major surgery within 4 weeks before first dose of study drug
* Previous serious infusion reactions or hypersensitivity to rituximab or bendamustine not controlled or prevented by steroid pre-medication
* Creatinine \> 2.0 mg/dL
* Total bilirubin \> 1.5 x upper limit of normal (ULN) (unless due to Gilbert's disease)
* Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \> 2.5 x ULN
* Absolute neutrophil count (ANC) \< 1000/mm\^3
* Platelets \< 50,000/mm\^3
* Lactating or pregnant