Zevalin Before Stem Cell Transplant in Treating Patients With Non-Hodgkin Lymphoma

Inclusion Criteria: * Histologically or cytologically confirmed relapsed cluster of differentiation (CD)20+ non-Hodgkin's lymphoma (NHL) (included in this category are follicular grade I, II, III, marginal zone, mantle cell, diffuse large B cell, small lymphocytic lymphoma) and CD20+ Hodgkin's disease for which standard curative therapy does not exist or is no longer effective * Patients must have had at least one prior chemotherapeutic regimen; steroids alone and local radiation do not count as regimens; radiotherapy must have been completed at least 4 weeks prior to entry into the study; Rituxan alone does not count as a regimen; however, Bexxar or Zevalin (ibritumomab tiuxetan) do and patients must have completed radioimmunotherapy (RIT) \> 12 months prior to enrollment * Karnofsky performance status of ≥ 60% * Life expectancy of greater than 3 months * Total bilirubin within institutional normal limits * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 times institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 ml/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Blood counts no restrictions * Patients who had anything less than a CR (PR, SD or progressive disease) to their last salvage regimen * Ability to understand and the willingness to sign a written informed consent document * Patients fit for non-myeloablative transplantation or best treatment that have an available matched (9/10 or better) related or unrelated donor * Patients who are considered rituximab refractory (defined as progression within 6 months of their last rituximab-containing regimen) Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study, rituximab within three months (unless there is evidence of progression), or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier are excluded; this does not include the use of steroids which may continue until two days prior to enrollment * Patients may not be receiving any other investigational agents * Failure to obtain insurance/payment authorization for Zevalin, unless the subject agrees to cover the cost * Patients with known active brain metastases, other neurological disorders/dysfunction or a history of seizure disorder, or other neurological dysfunction should be excluded from this clinical trial because of their poor prognosis * Patients who have an uncontrolled infection (presumed or documented) with progression after appropriate therapy for greater than one month * Patients with symptomatic coronary artery disease, uncontrolled congestive heart failure; left ventricular ejection fraction is not required to be measured, however if it is measured, patient is excluded if ejection fraction is \< 30% * Patients requiring supplementary continuous oxygen; diffusion capacity of the lung of carbon monoxide (DLCO) is not required to be measured, however if it is measured, patient is excluded if DLCO \< 35% * Patients with clinical or laboratory evidence of liver disease will be evaluated for the cause of liver disease, its clinical severity in terms of liver function and histology, and for the degree of portal hypertension * Patients with any of the following liver function abnormalities will be excluded: * Fulminant liver failure * Cirrhosis with evidence of portal hypertension or bridging fibrosis * Alcoholic hepatitis * Esophageal varices * A history of bleeding esophageal varices * Hepatic encephalopathy * Uncorrectable hepatic synthetic dysfunction evidenced by prolongation of the prothrombin time * Ascites related to portal hypertension * Chronic viral hepatitis with total serum bilirubin \> 3 mg/dL * Symptomatic biliary disease * Pregnant women are excluded from this study * Human immunodeficiency virus (HIV)-positive patients