RATIONALE: Giving monoclonal antibody therapy, radioimmunotherapy, and chemotherapy before a donor stem cell transplant helps stop the growth of cancer cells and helps stop the patient's immune system from rejecting the donor's stem cells. When the stem cells from a related donor that do not exactly match the patient's blood, are infused into the patient, they may help the patient's bone marrow make stem cells, red blood cells, white blood cells, and platelets. Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving tacrolimus and sirolimus before and after transplant may stop this from happening.

PURPOSE: This phase II trial is studying the side effects and how well giving indium In 111 ibritumomab tiuxetan and yttrium y 90 ibritumomab tiuxetan together with rituximab, fludarabine, melphalan, and donor stem cell transplant works in treating patients with B-cell non-Hodgkin lymphoma.

PRIMARY OBJECTIVES: I. To evaluate the safety and efficacy of a preparative regimen of Yttrium-90 (90^Y)- labeled anti-cluster of differentiation (CD)20 monoclonal antibody (MAb) (yttrium Y 90 ibritumomab tiuxetan) in combination with fludarabine (fludarabine phosphate) and melphalan followed by allogeneic hematopoietic stem cell transplant (APBSCT) for treatment of patients with B-cell low-grade non-Hodgkin lymphoma (LG NHL), intermediate-grade non-Hodgkin lymphoma (IG NHL) and mantle cell lymphoma (MCL). II. To evaluate the short- and long-term complications of this new preparative regimen, including rates of engraftment, acute and chronic graft-versus-host-disease (GVHD) and infectious complications. III. To estimate the disease response rate, disease relapse (progression) rate, and non-relapse mortality rate. IV. To perform exploratory studies that seek to measure/characterize the expression of costimulatory molecules and impact of these molecules on the natural killer (NK) and T cells of a subset of lymphoma patients pre- post- allogeneic stem cell transplant (ASCT) and the stem cell product from a portion of sibling donors.

OUTLINE: REDUCED-INTENSITY CONDITIONING: Patients receive rituximab intravenously (IV) followed by indium In-111 ibritumomab tiuxetan IV over 10 minutes on day -21 and rituximab IV followed by yttrium Y 90 ibritumomab tiuxetan IV over 10 minutes on day -14. Patients also receive fludarabine phosphate IV on days -9 to -5 and melphalan IV on day -4.

STEM CELL TRANSPLANTATION: Patients undergo APBSCT on day 0.

GVHD PROPHYLAXIS: Patients receive tacrolimus IV or orally (PO) and sirolimus PO beginning on day -3 and continuing for up to 6 months with taper.

After completion of study treatment, patients are followed up every 3 months for 1 year and then every 6 months for up to 5 years.

Inclusion Criteria:

• 6/6/human leukocyte antigen (HLA) matched sibling donor or related donor, or acceptable matched unrelated donor
• Biopsy (Bx) proven diagnosis of LG (including small lymphocytic lymphoma [SLL]/chronic lymphocytic leukemia [CLL], lymphoplasmacytic lymphoma, marginal zone, mucosa-associated lymphoid tissue [MALT] lymphoma and follicular lymphoma [FL] grade 1 and 2), IG (FL grade 3 and DLCL) or MCL NHL
• Prior demonstrated monoclonal CD20+ malignant B-Cell population in lymph nodes and/or BM Bx specimen
• LG NHL; must have relapsed after achieving a complete response (CR) or partial response (PR) to prior therapy or have never responded to prior therapy, including chemotherapy and/or MAb therapy
• MCL NHL in any disease state
• Other aggressive B-cell lymphomas (excluding Burkitt lymphoma or Burkitt-like lymphoma) having had at least one relapse or having been refractory to chemotherapy
• Bone marrow (BM) aspiration and Bx ( =< 42 days prior to imaging dose) which show < 25% lymphomatous involvement of total cellularity; in CLL, peripheral lymphocyte count < 5000/mm^3
• Salvage chemotherapy/MAbs to reduce BM lymphomatous involvement and reduce disease bulk allowed
• Normal renal function test with serum creatinine of =< 1.5 mg/dl, or a creatinine clearance of >= 60 ml/min
• Adequate pulmonary function as measured by forced expiratory volume in one second (FEV1) > 65% of predicted measured, or a diffusing capacity of carbon monoxide (DLCO) >= 50% of predicted measured
• Cardiac Ejection fraction of > 50% by Echocardiogram (ECHO) or multi gated acquisition (MUGA)
• Adequate liver function tests with a bilirubin of =< 1.5 x normal and serum glutamic oxaloacetic transaminase (SGOT) or serum glutamic pyruvic transaminase (SGPT) =< 2 x normal
• Negative Human Immunodeficiency Virus (HIV) antibody
• Karnofsky Performance Status (KPS) > 80
• No active Central Nervous System (CNS) disease or prior history of CNS disease
• Involved field External Beam Therapy (EBT) to area excluding lung, heat, liver, and kidney allowed, but evaluated on a case-by-case basis
• Recovery from last therapy and therapy dose (Y-90 Zevalin) must be >= 4 weeks from prior systemic chemotherapy
• DONOR: Age < 75 years
• DONOR: HLA genotypically identical related donor or acceptable matched unrelated donor
• DONOR: Must consent to G-CSF administration and leukapheresis for matched sibling donor, but for unrelated donor, the donor will sign a standard consent for donation at their designated donor or collection center
• DONOR: Must have adequate veins for leukapheresis or agree to placement of a Central Venous Catheter (CVC [femoral, subclavian])

Exclusion Criteria:

• Presence of Human Anti-Zevalin Antibody (HAZA)
• Prior radioimmunotherapy (RIT)
• Prior AHSCT; but prior aHSCT is allowed; prior fractionated total body irradiation (FTBI) in the conditioning regimen will be evaluated on an individual basis
• Prior malignancy, except for: adequately treated basal cell or squamous cell skin cancer; adequately treated noninvasive carcinomas; or other cancer from which the patient has been disease-free for at least 5 years; myelodysplastic syndromes (MDS) is excluded from this criterion
• Active evidence of Hepatitis B or C infection; hepatitis B surface antigen positive
• Total peripheral lymphocyte count > 5,000/mm^3 if SLL/CLL
• Burkitt lymphoma or Burkitt-like lymphoma
• DONOR: Age < 12 years
• DONOR: Identical twin
• DONOR: Pregnancy
• DONOR: HIV infection
• DONOR: Inability to achieve adequate venous access
• DONOR: Known allergy to G-CSF
• DONOR: Current serious systemic illness or any disease that may preclude the use of G-CSF (eg, recent thromboembolic event); for unrelated donors, considered ineligible by National Marrow Donor Program (NMDP) donor evaluation center