Study of Bendamustine Hydrochloride and Rituximab (BR) Compared With R-CVP or R-CHOP in the First-Line Treatment of Patients With Advanced Indolent Non-Hodgkin's Lymphoma (NHL) or Mantle Cell Lymphoma (MCL) - Referred to as the BRIGHT Study

Key Inclusion Criteria:

* Histopathologic confirmation of one of the following cluster of differentiation antigen 20 positive (CD20+) B-cell non-Hodgkin's lymphomas (tissue diagnostic procedures must be performed within 6 months of study entry and with biopsy material available for review):

  * follicular lymphoma (NCI CTCAE grade 1 or 2)
  * immunoplasmacytoma/immunocytoma (Waldenstrom's macroglobulinemia)
  * splenic marginal zone B-cell lymphoma
  * extra-nodal marginal zone lymphoma of mucosa-associated lymphoid tumor (MALT) type
  * nodal marginal zone B-cell lymphoma
  * mantle cell lymphoma
* Meets one of the following need-for-treatment criteria (with the exception of mantle cell lymphoma for which treatment is indicated):

  * presence of at least one of the following B-symptoms:

    1. fever (\>38ºC) of unclear etiology
    2. night sweats
    3. weight loss of greater than 10% within the prior 6 months
  * large tumor mass (bulky disease)
  * presence of lymphoma-related complications, including narrowing of ureters or bile ducts, tumor-related compression of a vital organ, lymphoma-induced pain, cytopenias related to lymphoma/leukemia, splenomegaly, pleural effusions, or ascites
  * hyperviscosity syndrome due to monoclonal gammopathy
* CD20+ B cells in lymph node biopsy or other lymphoma pathology specimen.
* No prior treatment (patients on "watch and wait" may enter the study if a recent biopsy \[obtained within the last 6 months\] is available)
* Adequate hematologic function (unless abnormalities related to lymphoma infiltration of the bone marrow or hypersplenism due to lymphoma) as follows:

  * hemoglobin of \>= 10.0 g/dL
  * absolute neutrophil count (ANC) \>=1.5\*10\^9/L
  * platelet count \>=100\*10\^9/L
* Bidimensionally measurable disease (field not previously radiated)
* Able to provide written informed consent
* Eastern Cooperative Oncology Group (ECOG) Performance Status \<=2
* Estimated life expectancy \>=6 months
* Serum creatinine of \<=2.0 mg/dL or creatinine clearance \>=50 mL/min
* Alanine aminotransferase (ALT) and aspartate transaminase (AST) ≤2.5\*upper limit of normal (ULN), and alkaline phosphatase and total bilirubin within normal limits
* Left ventricular ejection fraction (LVEF) \>= 50% by multiple gated acquisition scan (MUGA) or cardiac echocardiogram (ECHO), prior for any patient to be treated with R-CHOP
* A medically accepted method of contraception to be used by women of childbearing potential (not surgically sterile or at least 12 months naturally postmenopausal)
* Men capable of producing offspring and not surgically sterile must practice abstinence or use a barrier method of birth control.

Key Exclusion Criteria:

* Chronic lymphocytic leukemia, small lymphocytic lymphoma (SLL), or grade 3 follicular lymphoma
* Transformed disease (bone marrow blasts are permitted; however, transformed disease indicating leukemic involvement is not permitted)
* Central nervous system (CNS) lymphomatous involvement or leptomeningeal lymphoma
* Prior radiation for NHL, except for a single course of locally delimited radiation therapy with a radiation field not exceeding 2 adjacent lymph node regions
* Active malignancy, other than NHL, within the past 3 years except for localized prostate cancer treated with hormone therapy, cervical carcinoma in situ, breast cancer in situ, or non-melanoma skin cancer following definitive treatment
* New York Heart Association (NYHA) Class III or IV heart failure, arrhythmias or unstable angina, electrocardiograph (ECG) evidence of active ischemia or active conduction system abnormalities, or myocardial infarction within the last 6 months (prior to study entry, ECG abnormalities at screening must be documented by the investigator as not medically relevant)
* Known human immunodeficiency virus (HIV) positivity
* Active hepatitis B or hepatitis C infection (hepatitis B surface antigen testing required)
* Women who are pregnant or lactating
* Corticosteroids for treatment of lymphoma within 28 days of study entry Chronically administered low-dose corticosteroids (e.g., prednisone ≤20 mg/day) for indications other than lymphoma or lymphoma-related complications are permitted
* Any serious uncontrolled, medical or psychological disorder that would impair the ability of the patient to receive therapy
* Any condition which places the patient at unacceptable risk or confounds the ability of the investigators to interpret study data
* Any other investigational agent within 28 days of study entry
* Known hypersensitivity to bendamustine, mannitol, or other study-related drugs
* Ann Arbor stage I disease.