Phase 2 Poor Risk DLBCL of TLI and ATG Followed by Matched Allogeneic HT as Consolidation to Autologous HCT

INCLUSION CRITERIA * Age 18 to 70 years. * Histologically-proven diffuse large B-cell lymphoma (DLBCL) by the World Health Organization (WHO) classification. * Relapse after achieving initial remission or failure to achieve initial remission. Patients with residual radiographic abnormalities after primary therapy are eligible if abnormalities are postive by fluorodeoxyglucose (FDG)-positron emission tomography (PET) (FDG-PET). * Receipt of 2 cycles of second-line therapy and FDG-PET positive per Stanford (central) review. FDG-PET to be done 2 weeks after cycle 2 of second line chemotherapy. * Eastern Cooperative Oncology Group (ECOG) performance status \< 2 * Matched related or unrelated donor identified and available * Bone marrow biopsy and cytogenetic analysis within 8 weeks of registration * Pretreatment serum bilirubin \< 2 x the institutional upper limit of normal (ULN) * Serum creatinine \< 2 x the institutional ULN and measured or estimated creatinine clearance \> 60 mL/min by the following formula (all tests must be performed within 28 days prior to registration): * Estimated Creatinine Clearance = (140 age) x weight (kg) x 0.85 if female 72 x serum creatinine (mg/dL). * EKG within 42 days prior to registration with no significant abnormalities suggestive of active cardiac disease * Patients must have a radionuclide ejection fraction within 42 days of registration. If the ejection fraction is \< 40%, the patient will not be eligible. If the ejection fraction is 40-50%, the patient will have a cardiology consult. * Corrected diffusion capacity \> 55%. * Sexually active males are advised to use an accepted and effective method of birth control * Women of child-bearing potential are advised to use an accepted and effective method of birth control * Patients must sign and give written informed consent in accordance with institutional and federal guidelines. Patients must be informed of the investigational nature of this study. EXCLUSION CRITERIA * Known allergy to etoposide or a history of Grade 3 hemorrhagic cystitis with cyclophosphamide * Greater than Grade 2 sensory or motor peripheral neuropathy from prior vinca alkaloid use * Requiring therapy for coronary artery disease, cardiomyopathy, dysrhythmia, or congestive heart failure * Known to be human immunodeficiency virus (HIV)-positive. The antibody test for HIV must be performed within 42 days of registration. * Prior chemotherapy other than corticosteroids administered within 2 weeks of the initiation of protocol therapy. * Prior malignancy, except adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer or other cancer for which the patients has been disease-free for five years. * Prior diagnosis of non-Hodgkin's lymphoma * Active infection requiring oral or intravenous antibiotics * Prior autologous or allogeneic hematopoietic cell transplantation * Prior radioimmunotherapy * Pregnant * Lactating DONOR ELIGIBILITY * Related or unrelated HLA-identical donors who are in good health and have no contra-indication to donation * No contra-indication for the donor to collection by apheresis of mononuclear cells mobilized by G-CSF at a dose of 16 µg/kg of body weight. * Donors will be evaluated with a full history and physical examination. * Virology testing including HIV; cytomegalovirus (CMV); Epstein-Barr virus (EBV); human T-lymphotropic virus (HTLV); rapid plasma reagin (RPR); Hepatitis A, B and C be performed within 30 days of donation. * Prospective donors will be screened for CMV seroreactivity and seronegative donors will be utilized if available. * If more than one human leukocyte antigen (HLA)-matched related donor exists, then the donor will be selected on the basis of CD31 allotype.