RATIONALE: Giving low doses of chemotherapy, such as cyclophosphamide and fludarabine, total-body irradiation, and rituximab before a donor umbilical cord blood stem cell transplant helps stop the growth of cancer cells. It also stops the patient's immune system from rejecting the donor's stem cells. The donated stem cells may replace the patient's immune cells and help destroy any remaining cancer cells (graft-versus-tumor effect). Sometimes the transplanted cells from a donor can also make an immune response against the body's normal cells. Giving cyclosporine and mycophenolate mofetil after the transplant may stop this from happening.

PURPOSE: This phase II trial is studying how well giving chemotherapy and radiation therapy together with rituximab and an umbilical cord blood transplant works in treating patients with B-cell non-Hodgkin's lymphoma.

OBJECTIVES:

Primary

• Determine the overall and event-free survival at 1 year in patients with B-cell lymphoid malignancies treated with a nonmyeloablative conditioning regimen, rituximab, and umbilical cord blood (UCB) transplantation (UCBT).

Secondary

• Determine the speed of neutrophil and platelet recovery post allograft in these patients.
• Determine the incidence and speed of donor-derived engraftment and contribution of each UCB unit to engraftment in these patients.
• Determine the incidence and severity of acute graft-vs-host disease (GVHD) at 100 days in these patients.
• Determine the incidence and severity of chronic GVHD at 1 year in these patients.
• Determine the incidence of serious infectious complications and correlate with laboratory measurements of immune recovery in these patients.
• Determine the response to vaccination after UCBT in these patients.
• Determine the incidence of treatment-related mortality at 100 days and 180 days in these patients.
• Determine the incidence of malignant relapse or disease progression at 1 and 2 years in these patients.
• Determine the probabilities of overall and event-free survival at 2 years after UCBT in these patients.
• Determine the performance of laboratory studies investigating double-unit biology and correlate with unit engraftment in these patients.

OUTLINE:

• Pre-transplant rituximab therapy: Patients receive rituximab IV on days -8 or -7 and on day -4.
• Nonmyeloablative conditioning regimen: Patients receive fludarabine phosphate IV over 30 minutes on days -6 to -2 and cyclophosphamide IV on day -6. Patients also undergo total-body irradiation on day -1.
• Umbilical cord blood transplantation: Patients undergo umbilical cord blood transplantation on day 0. Patients receive filgrastim (G-CSF) IV or subcutaneously beginning on day 7 and continuing until blood counts recover.
• Post-transplant rituximab therapy: Patients receive rituximab IV on days 7, 14, 21, and 28.
• Graft-vs-host disease prophylaxis: Patients receive cyclosporine IV over 2-4 hours or orally twice daily on days -3 to 100, followed by a taper. Patients also receive mycophenolate mofetil IV or orally three times daily on days -3 to 45, followed by a taper.

Treatment continues in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed periodically for 5 years.

PROJECTED ACCRUAL: A total of 30 patients will be accrued for this study.

DISEASE CHARACTERISTICS:

• Diagnosis of 1 of the following:

  • CD20+* aggressive B-cell non-Hodgkin's lymphoma (NHL), including 1 of the following:

    • Diffuse large cell (DLC) NHL meeting 1 of the following criteria:

      • Relapsed disease after initial therapy but failed to mobilize or had bone marrow involvement and therefore is not suitable for an autologous stem cell transplantation
      • High-intermediate or high-risk, second-line, age-adjusted International Prognostic Index (IPI) score and in second complete remission (CR) or partial remission (PR) after prior autologous stem cell transplantation
      • Failed prior autologous stem cell transplantation and in at least PR after salvage chemotherapy

    • Large cell transformation of indolent NHL/chronic lymphocytic leukemia (CLL) meeting the following criteria:

      • CR/PR of the large cell component of disease after salvage chemotherapy or autologous stem cell transplantation

    • Mantle cell lymphoma meeting 1 of the following criteria:

      • High-risk, as defined by p53 positivity and in first CR/PR after initial therapy
      • Relapsed disease after initial therapy and in second or third CR/PR after salvage chemotherapy

  • CD20+* indolent NHL or CLL meeting the following criteria:

    • Must be in second or subsequent progression (pre-allograft cytoreduction necessary but CR/PR not required)

    • Indolent NHL includes, but is not limited to, any of the following:

      • Follicular NHL
      • Small cell NHL
      • Marginal zone NHL NOTE: *CD20 positivity must be demonstrated within the past 12 months

• Relapsed disease must be biopsy proven

• Prior pre-allograft cytoreduction may have included 1 of the following:

  • Single autologous stem cell transplantation with high-dose chemotherapy conditioning, if appropriate, and no conditioning prior to transplantation

  • Two or more courses of intensive combination chemotherapy (e.g., rituximab, irinotecan hydrochloride, cetuximab, epirubicin hydrochloride [RICE]) as appropriate according to diagnosis and prior therapy

    • Heavily pre-treated CLL patients in whom further combination chemotherapy is not appropriate may receive single-agent intermediate-dose cyclophosphamide for 2-3 courses

• No mantle cell or DLC NHL with progressive disease at allograft work-up

• No suitable matched related or unrelated donor available

• Two umbilical cord blood (UCB) units available meeting the following criteria:

  • Units and recipient must be ≥ 4/6 HLA-A and -B antigen and DRB1 allele matched
  • Each unit must have ≥ 1.5 x 10^7 total nucleated cells/recipient body weight

PATIENT CHARACTERISTICS:

• Karnofsky performance score 70-100%
• Creatinine clearance ≥ 50 mL/min
• Bilirubin < 2.5 mg/dL
• AST and ALT ≤ 3 times upper limit of normal (unless due to benign congenital hyperbilirubinemia)
• Spirometry and corrected DLCO ≥ 50% normal
• LVEF ≥ 40%
• Albumin ≥ 2.5 g/dL
• No active and uncontrolled infection at time of transplantation, including active infection with Aspergillus or other mold
• No HIV positivity
• Not pregnant or nursing
• Negative pregnancy test
• Fertile patients must use effective contraception

PRIOR CONCURRENT THERAPY:

• See Disease Characteristics
• No more than 120 days since prior autologous stem cell transplantation
• No more than 60 days since prior chemotherapy
• No prior allogeneic transplantation