A Phase I/II Study to Evaluate the Safety of Cellular Immunotherapy Using Autologous T Cells Engineered to Express a CD20-Specific Chimeric Antigen Receptor for Patients With Relapsed or Refractory B Cell Non-Hodgkin Lymphomas

* Recurrent disease after an initial response to MTX-based treatment

* Secondary CNS lymphoma:

* An inadequate rtesponse to at least 2 cycles of a MTX containing regimen, OR

* Recurrent disease after an initial response to MTX-based treatment

Patients must be 18 years of age or older, of any gender, race or ethnicity

Patients must be capable of understanding and providing a written informed consent

Negative serum pregnancy test within 2 weeks before enrollment for women of childbearing potential, defined as those who have not been surgically sterilized or who have not been free of menses for at least 1 year

Fertile male and female patients must be willing to use an effective contraceptive method before, during, and for at least 4 months after the CAR T cell infusion

Patients must have a Karnofsky performance status of \>= 60%

Confirmation of diagnosis by internal pathology review of initial or subsequent biopsy or other pathologic material at Fred Hutchinson Cancer Research Center (FHCRC)/Seattle Cancer Care Alliance (SCCA)/University of Washington (UW)/Harborview Medical Center (HMC)

Evidence of CD20 expression by immunohistochemistry or flow cytometry on the tumor specimen obtained with the biopsy performed with screening; if the CD20 expression on the screening tumor biopsy is unclear or could not be assessed due to technical reasons, CD20 expression on a concomitant tumor specimen (such as marrow biopsy or circulating tumor cells) may be used to satisfy this requirement. For CLL and lymphoplasmacytic lymphoma/Waldenström macroglobulinemia (WM) patients, the screening tumor biopsy can we waived for clinical reasons after discussion with the study principal investigator (PI). For patients with CNS lymphoma, a screening tumor biopsy is not required and evidence of CD20 expression can be documented from the original or prior biopsies

Serum creatinine =\< 2.5

Total bilirubin =\< 3.0 mg/dL

Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 5 x the upper limit of normal

Adequate pulmonary function, defined as =\< grade 1 dyspnea and saturated oxygen (SaO2) \>= 92% on room air; if pulmonary function test (PFT)s are performed based on the clinical judgment of the treating physician, patients with forced expiratory volume in 1 second (FEV1) \>= 50% of predicted and carbon monoxide diffusing capability (DLCO) (corrected) of \>= 40% of predicted will be eligible

Adequate cardiac function, defined as left ventricular ejection fraction (LVEF) of \>= 50% as assessed by echocardiogram or multigated acquisition (MUGA) scan, or LVEF of 45-49% and clearance by a cardiologist

Measurable disease that can be accurately measured in at least one dimension as \>= 1.5 cm with computed tomography (CT), ultrasound, or magnetic resonance imaging (MRI) techniques. Extranodal disease that is measurable by fludeoxyglucose F-18 (FDG)-positron emission tomography (PET) imaging only will also be allowed. Note that if an excisional biopsy was performed that removed the sole site of measurable disease, the patient will not be eligible for leukapheresis and generation of CAR T cell product

For patients with CNS lymphoma, a lesion \>= 1cm on brain or spine MRI is required

Active autoimmune disease requiring systemic immunosuppressive therapy

Patients requiring corticosteroid therapy at a dose of 15 mg or more per day of prednisone or the equivalent; pulsed corticosteroid dose for disease control is acceptable

Patients who are human immunodeficiency virus (HIV) seropositive

Women who are pregnant or breastfeeding

Significant cardiovascular diseases within the past 6 months including uncontrolled congestive heart failure (\> New York Heart Association \[NYHA\] class II), myocardial infarction, unstable angina, or uncontrolled arrhythmia

History of severe immediate hypersensitivity reaction to cyclophosphamide or fludarabine

History or presence of clinically relevant non-lymphoma central nervous system pathology, including seizures that are uncontrolled on anticonvulsant therapy (\>= 1 seizure in the last year), paresis, aphasia, stroke, severe brain injuries, dementia, Parkinson disease, cerebellar disease, or psychosis

Treatment with any investigational agent on a different clinical trial within 4 weeks prior to enrollment, unless the patient is documented to be unresponsive to the therapy and at least 3 half-lives have elapsed prior to enrollment

Treatment with any anti-CD19 or anti-CD20 antibody or antibody-drug conjugate therapy within 4 weeks before enrollment

Previous treatment with CD19-targeted CAR T cells that has resulted in ongoing B cell aplasia at the time of enrollment; patients that demonstrate recovery of normal B cells (\>= 20 B cells/ul) by flow cytometry at any point 28 days or later after CD19 CAR T cell infusion will be considered to have functional loss of CD19 CAR T cells and are potentially eligible

Patients with systemic disease without radiologic evidence of CNS involvement and with isolated CSF involvement detectable by flow cytometry are eligible for enrollment in systemic disease cohorts if neurologically asymptomatic. CSF involvement is not an exclusion for patients enrolled as a primary or secondary CNS lymphoma.

Presence of active acute or chronic graft versus host disease (GVHD)

Uncontrolled active infection (bacterial, fungal, viral, mycobacterial) not responding to treatment with intravenous antibiotics, antiviral or antifungal agents

Patients with concurrent known additional malignancy that is progressing and/or requires active treatment; exceptions include squamous or basal cell carcinoma of the skin and low grade prostate carcinoma (Gleason grade =\< 6). Maintenance anti-hormone therapies for breast or prostate cancers are allowed and are not considered active treatment

Patients with blood or platelet transfusion within 1 week prior to signing Consent A, or with platelets \< 50,000/mm\^3, neutrophils \< 750/mm\^3, or hemoglobin \< 8.5 g/dL, unless the cytopenias are considered by the treating physician to be largely due to marrow involvement by lymphoma

What this study is about