Autologous Stem Cell Transplant Followed by Donor Stem Cell Transplant in Treating Patients With Relapsed or Refractory Lymphoma

Inclusion Criteria: Patients with lymphoma (non-Hodgkin lymphoma [NHL], chronic lymphocytic leukemia/small lymphocytic lymphoma [CLL/SLL] or Hodgkin's lymphoma) with primary refractory or relapsed disease after standard chemotherapy at high risk of relapse with conventional autografting; patients with a diagnosis of CLL (or small lymphocytic lymphoma) or diagnosis of CLL that progresses to prolymphocytic leukemia (PLL), or T-cell CLL or PLL Must have an HLA genotypically or phenotypically identical related donor or, at a minimum, a high likelihood of identifying an HLA-matched unrelated donor; the determination of availability of a suitable unrelated donor may be based on a World-Book search Cross-over to other tandem autologous-allogeneic research protocol (#2241) will be allowed if the patient loses the suitable HLA-matched related or unrelated donor but has an available HLA-haploidentical donor before receiving the allogeneic transplantation and if the patient meets the eligibility criteria of the subsequent study Cross-over from other tandem autologous-allogeneic research protocol (#2241) will be allowed if a suitable HLA-matched related or unrelated donor is identified before receiving the allogeneic transplantation and if the patient meets the eligibility criteria of the subsequent study Signed informed consent Detectable tumor on radiographic studies or bone marrow biopsy prior to mobilization regimen Expected survival >= 3 months from study entry DONOR: HLA genotypically or phenotypically identical related donor DONOR: Must consent to granulocyte-colony stimulating factor (G-CSF) (filgrastim) administration and leukapheresis for both PBSC allograft and subsequent donor lymphocyte infusion (DLI) DONOR: Must have adequate veins for leukapheresis or agree to placement of central venous catheter (femoral or subclavian) DONOR: Age < 75 years (yrs), older donors may be considered after review at Patient Care Conference DONOR: Fred Hutchinson Cancer Research Center (FHCRC) matching allowed will be grades 1.0 to 2.1; unrelated donors who are prospectively: matched for HLA-A, B, C, DRB1 and DQB1 by high resolution typing; only a single allele disparity will be allowed for HLA-A, B, or C as defined by high resolution typing DONOR: Donors are excluded when preexisting immunoreactivity is identified that would jeopardize donor hematopoietic cell engraftment; this determination is based on the standard practice of the individual institution; the recommended procedure for patients with 10 of 10 HLA allele level (phenotypic) match is to obtain a panel reactive antibody (PRA) screens to class I and class II antigens for all patients before HCT; if the PRA shows > 10% activity, then flow cytometric or B and T cell cytotoxic cross matches should be obtained; the donor should be excluded if any of the cytotoxic cross match assays are positive; for those patients with an HLA class I allele mismatch, flow cytometric or B and T cell cytotoxic cross matches should be obtained regardless of the PRA results; a positive anti-donor cytotoxic crossmatch is an absolute donor exclusion DONOR: Patient and donor pairs homozygous at a mismatched allele in the graft rejection vector are considered a two-allele mismatch, i.e., the patient is A*0101 and the donor is A*0102, and this type of mismatch is not allowed DONOR: Only G-CSF mobilized peripheral blood mononuclear cells (PBMC) only will be permitted as a hematopoietic stem cell (HSC) source on this protocol Exclusion Criteria: Life expectancy severely limited by disease other than lymphoma Prior autologous hematopoietic stem cell transplant Patients at high risk of veno-occlusive disease of the liver (criteria not yet rigorously defined but includes bilirubin > 2.0 mg and serum glutamic oxaloacetic transaminase [SGOT] or serum glutamate pyruvate transaminase [SGPT] > 2 x normal); patients may be accepted outside of this range if cleared by gastrointestinal (GI) consult Cardiac ejection fraction (EF) < 40% on multi-gated acquisition (MUGA) scan or cardiac echocardiogram (echo) (or if unable to obtain ejection fraction, shortening fraction of < 26%); patients with active or a history of cardiac disease should be evaluated with appropriate cardiac studies and/or consult; ejection fraction is required if age > 50 years or there is a history of anthracyclines or history of cardiac disease; patients with a shortening fraction < 26% may be enrolled if approved by a cardiologist Baseline serum-creatinine > 2.0 mg/dl and a calculated or measured creatinine clearance of < 50 ml/minute Seropositive for the human immunodeficiency virus (HIV) Pulmonary dysfunction as measured by a corrected diffusing capacity of the lung for carbon monoxide (DLCO) < 50% of predicted total lung capacity (TLC) < 30%, forced expiratory volume in 1 second (FEV1) < 30% and/or receiving supplementary continuous oxygen; the FHCRC principal investigator (PI) of the study must approve enrollment of all patients with pulmonary nodules Pregnancy or breast-feeding Patients with poorly controlled hypertension despite hypertensive medication Karnofsky score less than 60; pediatric criteria: Lansky Play-Performance Score < 40 Patients with cluster of differentiation (CD)34 selected auto grafts Patients with active non-hematologic malignancies (except non-melanoma skin cancers); this exclusion does not apply to patients with non-hematologic malignancies that do not require therapy Patients with a history of non-hematologic malignancies (except non-melanoma skin cancers) currently in a complete remission, who are less than 5 years from the time of complete remission, and have a > 20% risk of disease recurrence; this exclusion does not apply to patients with non-hematologic malignancies that do not require therapy DONOR: Identical twin DONOR: Age less than 12 years DONOR: Pregnancy DONOR: Human immunodeficiency virus (HIV) seropositivity DONOR: Inability to achieve adequate venous access DONOR: Known allergy to G-CSF DONOR: Current serious systemic illness DONOR: Failure to meet FHCRC criteria for stem cell donation DONOR: Donor (or centers) who will exclusively donate marrow