Stage II, III or IV disease as defined by the Ann Arbor Staging System Ann Arbor stage II-IV disease (Stage I primary mediastinal B-cell lymphoma will also be eligible) Histologically confirmed CD-positive, CD-positive untreated primary mediastinal B-cell lymphoma (any Ann Arbor stage), diffuse large B-cell lymphoma (Ann Arbor stage III or IV), or grey zone lymphoma (any Ann Arbor stage); patients with heterogeneous, weak or equivocal CD staining will also be included (no specific cut off percentage for CD stain is required) Stages II, III, or IV (Ann Arbor Staging) NHL (Part and ): Intermediate or high risk by Ann Arbor Staging with Cotswald Modifications that meets criteria for active disease requiring therapy. Ann Arbor stage II-IV Patients with histologically-confirmed Low Tumor Burden Follicular Lymphoma, without B symptoms, Ann Arbor stage II to IVA NHL (CD+ FL of Grades , , or a) Ann Arbor stage I - stage IV DLBCL at the time of relapsed/refractory disease to be eligible Ann Arbor stage I or II disease Ann Arbor Stage II, III or IV At least one adverse prognostic factor: \r\n* Initial relapse =< months after primary chemotherapy\r\n* Staged as Ann Arbor classification initial stage III or IV disease\r\n* Chemotherapy resistant disease\r\n* Failure to achieve a complete response (CR) with cytoreductive chemotherapy or persistent positive fludeoxyglucose F (FDG)-positron emission tomography (PET) imaging Patients must have non-bulky stage I or II disease by Ann Arbor classification\r\n* This staging excludes fludeoxyglucose F (FDG)-PET evaluation\r\n* Patients who have stage I or II non-bulky disease based on diagnostic CT scan, but are upstaged to stage III or IV based on FDG-PET evaluation, are also eligible\r\n* Stage and bulk are assigned using measurements obtained prior to biopsy Collection of a ml blood sample (red top for serum) from the patient for Ann Arbor Scoring and ready to be shipped immediately after randomization. Stages II bulky disease (defined as mass size of more than cm), stage III, or IV (Ann Arbor staging); patients with stage I and stage II non-bulky disease are excluded from this study Ann Arbor stage II to IV. Ann Arbor stage or or stage with bulky disease Stage III/IV disease by Ann Arbor Staging Ann Arbor stage IIB, IIIB, IVA, or IVB Stage II (not candidates for local x-ray therapy), III, or IV disease by the Ann Arbor Classification Information available for calculation of International Prognostic Score (IPS): age, gender; albumin, white blood cell (WBC) count, hemoglobin, lymphocyte count, and stage of disease according to Ann Arbor classification Stage II, III, and IV disease by Ann Arbor classification Ann Arbor Stage I disease Histologically confirmed diagnosis of follicular lymphoma CD+ (Grade , or a) Ann Arbor Stage II, III or IV disease. Stage III or IV disease at any time in the past (Ann Arbor Staging System for Non-Hodgkins Lymphomas) Ann Arbor Stage II, III, or IV Stage must be classified as one of the following:\r\n* Ann Arbor stage IA or IIA with:\r\n** Non-bulky mediastinal disease (< % mediastinal to thoracic ratio on chest x-ray [CXR])\r\n** < nodal regions involved on the same side of the diaphragm\r\n** No E lesion Stage II, III or IV (Ann Arbor Staging) Ann Arbor stage I disease. Ann Arbor stage III or IV disease at diagnosis or at relapse/refractory disease confirmation Ann Arbor stage III or IV disease (Cohort A only)