Monoclonal Antibody Therapy, Combination Chemotherapy, and Peripheral Stem Cell Transplant in Non-Hodgkin's Lymphoma

Inclusion Criteria: * Diagnosis of non-Hodgkin's lymphoma (NHL) of one of the following types: * Diffuse large B-cell * Composite (at least 50% of tumor showing diffuse histology) * Diffuse mixed cell * Immunoblastic * Relapsed or refractory disease sensitive to initial or subsequent conventional therapy (at least a partial response) * Eligible for high-dose carmustine, etoposide, cytarabine, and melphalan protocol and autologous bone marrow transplantation or peripheral blood stem cell transplantation * Evidence of CD20 antigen expression in tumor tissue * Bidimensionally measurable disease * Adequate peripheral blood stem cells * At least 15,000,000 CD34+ cells/kg or * At least 25,000 granulocyte macrophage colony-forming units/kg * Age: 19 to 70 * Performance status: Karnofsky 70-100% * Life expectancy: at least 4 months post-transplantation * Bilirubin less than 2.0 mg/dL * Creatinine less than 2.0 mg/dL * Cardiac ejection fraction at least 40% for any of the following criteria: * Age 60 and over * Significant cardiac history (myocardial infarction or congestive heart failure) * Received greater than 350 mg/m\^2 of prior doxorubicin * DLCO at least 50% of predicted * HIV negative * Fertile patients must use effective contraception during and for at least 6 months after study participation * At least 4 weeks since prior biologic therapy and recovered * Human antimouse antibody negative * At least 4 weeks since prior cytotoxic chemotherapy and recovered * At least 4 weeks since prior radiotherapy and recovered * At least 4 weeks since prior immunosuppressants and recovered Exclusion Criteria: * No progressive disease in a field that has been previously irradiated with more than 3,500 cGy within the past year * No known brain or leptomeningeal metastases * No active obstructive hydronephrosis * No New York Heart Association class III or IV heart disease * No evidence of severe organ dysfunction * No other major medical illnesses * No active infection requiring IV antibiotics * No other malignancy within the past 5 years except adequately treated skin cancer or carcinoma in situ of the cervix * Not pregnant/negative pregnancy test * No prior peripheral blood stem cell transplantation following high-dose chemotherapy or chemoradiotherapy * No other concurrent biologic therapy for NHL * No concurrent steroids except maintenance-dose steroids for noncancerous disease * No concurrent external beam radiotherapy for NHL * No other concurrent participation on protocol involving non-FDA-approved drugs or biologics