This phase I/II trial studies how well autologous stem cell transplant followed by donor stem cell transplant works in treating patients with lymphoma that has returned or does not respond to treatment. Peripheral blood stem cell transplant using stem cells from the patient or a donor may be able to replace immune cells that were destroyed by chemotherapy used to kill cancer cells. The donated stem cells may also help destroy any remaining cancer cells (graft-versus-tumor effect).

PRIMARY OBJECTIVES:

I. To evaluate engraftment of human leukocyte antibody (HLA) identical peripheral blood stem cell (PBSC) allografts given after conditioning with total-body irradiation (TBI) (200cGy) +/- fludarabine (fludarabine phosphate), 90 mg/m^2 and post-grafting immunosuppression with cyclosporine (CSP)/mycophenolate mofetil (MMF) in refractory or relapsed lymphoma patients following an initial autologous peripheral blood stem cell transplant (PBSCT) for disease cytoreduction.

II. To determine the non-relapse mortality at day 100 post-non-myeloablative allografting following mobilization and high-dose chemotherapy with autografting.

SECONDARY OBJECTIVES:

I. To determine the disease free survival and overall survival of non-myeloablative allografting following autologous PBSCT.

OUTLINE:

CONDITIONING REGIMEN: Patients with matched, related stem cell donors receive cyclophosphamide intravenously (IV) on days -6 and -5 and undergo TBI twice daily (BID) on days -3 to -1. Patients with matched, unrelated stem cell donors receive carmustine IV over 3 hours on day -7, etoposide IV over 2 hours BID on days -6 to -3, and cytarabine IV over 3 hours BID on days -6 to -3, and melphalan IV over 30 minutes on day -2.

TRANSPLANTATION: All patients undergo autologous PBSCT on day 0.

NON-MYELOABLATIVE CONDITIONING: Beginning 40-120 days following PBSC transplant, patients with related donors undergo TBI on day 0. Patients with unrelated donors receive fludarabine phosphate IV over 30 minutes on days -4 to -2 and undergo TBI on day 0.

TRANSPLANTATION: Patients undergo non-myeloablative allogeneic PBSCT on day 0.

IMMUNOSUPPRESSION: Patients receive cyclosporine orally (PO) BID on days -3 to 56 (patients with related donors) or 100 (patients with unrelated donors) followed by taper to day 180. Patients also receive mycophenolate mofetil PO BID on days 0-27 (patients with related donors) or thrice daily (TID) on days 0-27, then BID on days 28-40 followed by taper to day 96 (patients with unrelated donors).

Some patients may undergo donor lymphocyte infusion if there is evidence of disease progression and no evidence of graft-vs-host disease (GVHD).

After completion of study treatment, patients are followed up at day 180, 1 year, 1.5 years, 2 years, 3 years, and then annually thereafter.

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