Chemotherapy, Total-Body Irradiation, Rituximab, and Donor Stem Cell Transplant in Treating Patients With B-Cell Non-Hodgkin's Lymphoma or Chronic Lymphocytic Leukemia

DISEASE CHARACTERISTICS: * Diagnosis of 1 of the following: * CD20-positive aggressive B-cell non-Hodgkin's lymphoma (NHL), including any of the following subtypes: * Diffuse large cell lymphoma\*, meeting 1 of the following criteria: * Relapsed disease after initial therapy, but failed to mobilize or had bone marrow involvement and therefore is not suitable for an autologous stem cell transplantation * High-intermediate- or high-risk second-line, age-adjusted International Prognostic Index score and in second complete remission (CR) or partial remission (PR) after autologous stem cell transplantation * Failed prior autologous stem cell transplantation and in PR or better after salvage chemotherapy * Large cell transformation of indolent NHL or chronic lymphocytic leukemia (CLL), meeting the following criteria: * In CR or PR of the large cell component of disease after salvage chemotherapy or autologous stem cell transplantation * Mantle cell lymphoma\*, meeting 1 of the following criteria: * High-risk disease (e.g., p53 positivity) and in first CR or PR after initial therapy * Relapsed disease after initial therapy and in second or third CR or PR after salvage chemotherapy NOTE: \*No progressive disease at allograft work-up * CD20-positive indolent NHL (e.g., follicular lymphoma, small cell lymphoma, or marginal zone NHL) OR CLL * Second or subsequent progression (pre-allograft cytoreduction necessary, but CR or PR not required) * Relapsed disease must be biopsy-proven * Must have received pre-allograft salvage chemotherapy, including 1 of the following: * Single autologous stem cell transplantation using high-dose chemotherapy conditioning within the past 120 days * At least 2 courses of intensive combination chemotherapy (e.g., RICE \[rituximab, ifosfamide, carboplatin, etoposide\]), according to diagnosis, within the past 80 days * CLL patients who have received CAMPATH do not have to receive pre-allograft salvage chemotherapy * HLA-compatible related or unrelated donor available * HLA-matched ≥ 9/10 of the A, B, C, DRB1, and DQB1 loci, as tested by high resolution typing * One allele mismatch allowed PATIENT CHARACTERISTICS: * Karnofsky performance status 70-100% * Creatinine \< 1.2 mg/mL OR creatinine clearance ≥ 50 mL/min * Bilirubin \< 2.5 mg/dL * AST and ALT ≤ 3 times upper limit of normal (unless benign congenital hyperbilirubinemia is present) * Spirometry and corrected DLCO ≥ 50% of normal * LVEF ≥ 40% * Albumin ≥ 2.5 g/dL * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No active uncontrolled infection, including active infection with Aspergillus or other mold * No HIV infection * No hepatitis B antibody or antigen positivity PRIOR CONCURRENT THERAPY: * See Disease Characteristics * No prior allogeneic transplantation