Inclusion Criteria:

• Patients with lymphoma (non-Hodgkin lymphoma [NHL], chronic lymphocytic leukemia/small lymphocytic lymphoma [CLL/SLL] or Hodgkin 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 G-CSF 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 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 glutamic 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 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 primary investigator (PI) of the study must approve enrollment of all patients with pulmonary nodules
• Pregnancy or breast-feeding
• Radiation therapy to mediastinum within 3 months prior to enrollment
• Patients with poorly controlled hypertension despite hypertensive medication
• Karnofsky score < 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 nonmelanoma 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 nonmelanoma 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: 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