A Phase II Study of Allo-HCT for B-Cell NHL Using Zevalin, Fludarabine and Melphalan

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) \>…