Umbilical Cord Blood NK Cells, Rituximab, High-Dose Chemotherapy, and Stem Cell Transplant in Treating Patients With Recurrent or Refractory B-Cell Non-Hodgkin's Lymphoma

This phase II trial studies the side effects of cord blood-derived expanded allogeneic natural killer cells (umbilical cord blood natural killer \[NK\] cells), rituximab, high-dose chemotherapy, and stem cell transplant in treating patients with B-cell non-Hodgkin's lymphoma that has come back (recurrent) or that does not respond to treatment (refractory). Immune system cells, such as cord blood-derived expanded allogeneic natural killer cells, are made by the body to attack foreign or cancerous cells. Immunotherapy with rituximab, may induce changes in body's immune system and may interfere with the ability of tumor cells to grow and spread. Drugs used in chemotherapy, such as carmustine, cytarabine, etoposide, lenalidomide, melphalan, and rituximab, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. A stem cell transplant using stem cells from the patient or a donor may be able to replace blood-forming cells that were destroyed by chemotherapy used to kill cancer cells. The donated stem cells may also replace the patient's immune cells and help destroy any remaining cancer cells. Giving cord blood-derived expanded allogeneic natural killer cells, rituximab, high-dose chemotherapy, and stem cell transplant may work better in treating patients with recurrent or refractory B-cell non-Hodgkin's lymphoma.

PRIMARY OBJECTIVE:

I. To establish the safety of this treatment by determining its treatment-related mortality (TRM) within 30 days.

SECONDARY OBJECTIVES:

I. To estimate the relapse-free survival (RFS). II. To estimate the overall survival (OS). III. To quantify duration of infused allogeneic umbilical cord blood (UCB)-derived natural killer (NK) cells in the recipient.

OUTLINE:

PREPARATIVE REGIMEN: Patients receive carmustine intravenously (IV) over 2 hours on day -12, etoposide IV twice daily (BID) over 3 hours on days -11 to -8, cytarabine IV BID over 1 hour on days -11 to -8, melphalan IV over 30 minutes on day -7, and lenalidomide orally (PO) once daily (QD) on days -7 to -2 in the absence of disease progression or unacceptable toxicity. Patients who are CD20+ also receive rituximab IV over 3 hours on days -13 and -7.

NK-CELL INFUSION: Patients receive cord blood-derived expanded allogeneic NK cells IV over 1 hour on day -5 in the absence of disease progression or unacceptable toxicity.

STEM CELL TRANSPLANT: Patients undergo stem cell transplant IV over 30-60 minutes on day 0 in the absence of disease progression or unacceptable toxicity.

POST-TRANSPLANT: Patients receive filgrastim subcutaneously (SC) QD beginning on day +5. Treatment continues until white blood cell count recovers in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up at 30, 100, and 180 days.

Eligibility Criteria:
Inclusion Criteria:

* Patients with B-cell lymphoma who are candidates to autologous stem-cell transplantation:

  * Primary refractory or relapsed diffuse large B-cell lymphoma in response to salvage treatment
  * Primary refractory or relapsed follicular lymphoma or other indolent B-cell histology in response to salvage treatment
  * Chemosensitive mantle-cell lymphoma in first or later line of treatment
* Estimated serum creatinine clearance \>= 60 ml/min and a normal serum creatinine for age
* Serum glutamic-oxaloacetic transaminase (SGOT) and/or serum glutamate pyruvate transaminase (SGPT) =\< 3 x upper limit of normal (ULN)
* Total bilirubin and alkaline phosphatase (ALP) =\< 2 x ULN or =\< 3 x ULN for Gilbert's disease
* Forced expiratory volume in one second (FEV1), forced vital capacity (FVC) and diffusion lung capacity (DLCO) (corrected for hemoglobin \[Hgb\]) \>= 50% of the predicted value
* Left ventricular ejection fraction \>= 40%. No uncontrolled arrhythmias or symptomatic cardiac disease
* Performance status \< 2 (Eastern Cooperative Oncology Group \[ECOG\])
* Negative beta human chorionic gonadotropin (HCG) in woman with child-bearing potential

Exclusion Criteria:

* Primary central nervous system (CNS) lymphoma
* Grade \>= 3 non-hematologic toxicity from prior therapy that has not resolved to =\< grade (G) 1
* Prior whole brain irradiation
* Active hepatitis B, either active carrier (hepatitis B surface antigen positive \[HBsAg +\]) or viremic (hepatitis B virus \[HBV\] deoxyribonucleic acid \[DNA\] \>= 10,000 copies/mL, or \>= 2,000 IU/mL)
* Evidence of either cirrhosis or stage 3-4 liver fibrosis in patients with chronic hepatitis C or positive hepatitis C serology
* Active infection requiring parenteral antibiotics
* Human immunodeficiency virus (HIV) infection
* Radiation therapy in the month prior to enroll
* Breastfeeding females