Chemotherapy, Radiation Therapy, Rituximab, and Umbilical Cord Blood Transplant in Treating Patients With B-Cell Non-Hodgkin's Lymphoma

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