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)

- DONOR INCLUSION CRITERIA FOR TLI/ANTITHYMOCYTE GLOBULIN (ATG):

- Donors phenotypically (8/8) or genotypically (8/8 by high resolution typing) matched
by human leukocyte antigen (HLA) typing; a single allele (by high resolution typing)
mismatch is allowed to proceed

- Donor must consent to undergo filgrastim (G-CSF) administration and leukapheresis for
peripheral blood stem cell (PBSC) allograft

- Donor must have adequate veins for apheresis or agree to placement of central venous
catheter (femoral, subclavian)

- Deemed medically fit for G-CSF administration and leukapheresis

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

- DONOR EXCLUSION CRITERIA FOR TLI/ATG:

- Identical twin

- Patient and donor pairs with a serologic mismatch (e.g., the patient is A*0101 and
the donor is A*0201, if all other antigens match)

- Donors with a positive anti-recipient cytotoxic crossmatch, if tested

- Donors who are pregnant or breastfeeding

- Donors who are HIV seropositive

- Donors with inadequate venous access

- Donors with known adverse reaction to G-CSF

- Donors with current serious systemic illness

- Donors with an uncontrolled infection

- Donors receiving experimental therapy or investigational agents

- Donors with prior or concurrent malignancies except localized non-melanoma skin
malignancies or treated cervical carcinoma in situ; cancer treated with curative
intent < 5 years previously will not be allowed; cancer treated with curative intent
> 5 years previously will be allowed