Inclusion Criteria:

          -  Patients must have a histologically confirmed diagnosis of aggressive B-cell lymphoma
             (diffuse large B-cell lymphoma [DLBCL], Burkitt lymphoma [BL], etc.) expressing the
             CD20 antigen and have failed at least one prior standard systemic therapy

          -  Patients must have relapsed after high-dose therapy and autologous transplantation or
             be ineligible for high-dose therapy and autologous transplantation; patients that have
             failed autologous transplantation are those with persistent disease > 30 days after
             transplant; those ineligible for autologous transplant include those with
             chemoresistant disease (i.e., patients who have not achieved a partial response or
             better with their most recent chemotherapy regimen), are expected to have a poor
             outcome from autologous transplant (e.g., DLBCL relapsing within one year of
             rituximab, cyclophosphamide, doxorubicin hydrochloride, vincristine sulfate,
             prednisone [R-CHOP]-like chemotherapy, double hit lymphoma, v-myc myelocytomatosis
             viral oncogene homolog (avian) positive [MYC+] lymphoma, persistent positron emission
             tomography [PET] positivity after chemotherapy), are unable to collect sufficient or
             tumor-free autologous stem cells per Seattle Cancer Care Alliance (SCCA) standard
             practice, are unable to tolerate the high-dose autologous conditioning regimens, or
             who refuse a high-dose autologous transplant regimen

          -  Creatinine (Cr) < 2.0

          -  Bilirubin < 1.5 mg/dL with the exception of patients thought to have Gilbert's
             syndrome, who may have a total bilirubin above 1.5 mg/dL

          -  Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) < 3 x upper limit of
             normal (ULN)

          -  Patients must have an expected survival without treatment of > 60 days and must be
             free of major infection including human immunodeficiency virus (HIV)

          -  Patients must have an HLA-identical related or HLA-matched unrelated donor

        Exclusion Criteria:

          -  Receipt of systemic anti-lymphoma therapy withinthe following intervals prior to the
             therapeutic 90Y-ibritumomab tiuxetan dose:

               -  < 30 days for intravenously-administered cytotoxic chemotherapy and/or monoclonal
                  antibodies

               -  < 5 half-lives for all other anti-cancer agents (e.g., targeted therapies,
                  corticosteroids, immunomodulatory agents, etc.)

          -  Inability to understand or give an informed consent

          -  Active central nervous system lymphoma

          -  Pregnancy

          -  Fertile men or women unwilling to use contraceptive techniques during and for 12
             months following treatment

          -  Southwest Oncology Group (SWOG)/Eastern Cooperative Oncology Group (ECOG) performance
             score >= 2

          -  High-dose chemotherapy or external beam radiation therapy to lung, liver, or kidneys >
             20 Gy within the previous 100 days prior to therapeutic 90Y-ibritumomab tiuxetan dose

          -  Medical condition that would contraindicate allogeneic transplantation as per standard
             practice guidelines (e.g., impaired cardiopulmonary function, hepatitis, etc)