Genetically Modified T-cells (CMV-Specific CD19-CAR T-cells) Plus a Vaccine (CMV-MVA Triplex) for the Treatment of Intermediate or High Grade B-Cell Non-Hodgkin Lymphoma

This phase I trial studies the safety and feasibility of cytomegalovirus (CMV) specific CD19-chimeric antigen receptor (CAR) T cells in combination with the CMV-modified vaccinia Ankara (MVA) triplex vaccine following lymphodepletion in treating patients with intermediate or high grade B-cell non-Hodgkin lymphoma (NHL) that has come back after a period of improvement (relapsed) or that does not respond to treatment (refectory). CAR T cells are a type of treatment in which a patient's T cells (a type of immune system cell) are changed in the laboratory so they will attack cancer cells. T cells are taken from a patient's blood. Then the gene for a special receptor that binds to a certain protein on the patient's cancer cells is added in the laboratory. The special receptor is called CAR. Large numbers of the CAR T cells are grown in the laboratory and given to the patient by infusion. Vaccines such as CMV-MVA triplex are made from gene-modified viruses and may help the body build an effective immune response to kill cancer cells. Giving CMV-specific CD19-CAR T-cells plus the CMV-MVA triplex vaccine may help prevent the cancer from coming back.

PRIMARY OBJECTIVE:

I. Assess the safety and describe the toxicity profile of anti-CD19-CAR CMV-specific T-lymphocytes (CMV-specific CD19-CAR T cells) as monotherapy and when given in combination with a multi-peptide CMV-modified vaccinia Ankara vaccine (CMV-MVA Triplex) following standard of care lymphodepletion.

SECONDARY OBJECTIVES:

I. Determine the feasibility of autologous CMV-specific CD19-CAR T cell manufacturing, as assessed by the ability to meet the required cell dose and product release requirements.

II. Estimate the overall and complete disease response rate at days 28 and 84 after CAR T cell infusion.

III. Determine short- and longer-term CMV-specific CD19-CAR T cell in vivo expansion and persistence.

IV. Assess whether the CMV-specific CD19-CAR T cells respond to CMV-MVA Triplex vaccine.

V. Estimate the rate of CMV reactivation after CAR T cell. VI. Estimate the one-year progression-free survival (PFS) rate and median overall survival (OS) post-CAR T cell infusion.

EXPLORATORY OBJECTIVE:

I. Assess whether the CMV-specific CD19-CAR T cells respond to CMV-MVA Triplex vaccine when administered to participants that received CAR T cells only in the safety lead-in portion in the expansion phased of the study (i.e., once safety of the CMV-MVA Triplex vaccine is established in the feasibility portion of the study).

OUTLINE: This is a dose-escalation study of CMV-specific CD19-CAR T cells followed by a dose-expansion study.

Patients undergo leukapheresis on day -30 and receive lymphodepleting chemotherapy on days -10 to -3 per standard of care (SOC) on study. Patients then receive CMV-specific CD19-CAR T cells intravenously (IV) on day 0 and CMV-MVA triplex vaccine intramuscularly (IM) on days 28 and 56 in the absence of unacceptable toxicity on study. Patients also undergo x-ray during screening and on study, as well as positron emission tomography (PET), computed tomography (CT), magnetic resonance imaging (MRI), blood sample collection, and bone marrow biopsy on study and during follow-up.

Eligibility Criteria:
Inclusion Criteria:

* Documented informed consent of the participant and/or legally authorized representative

  * Assent, when appropriate, will be obtained per institutional guidelines
* Agreement to allow the use of archival tissue from diagnostic tumor biopsies

  * If unavailable, exceptions may be granted with study principal investigator (PI) approval
* Note: For research participants who do not speak English, a short form consent may be used with a City of Hope (COH) certified interpreter/translator to proceed with screening and leukapheresis, while the request for a translated full consent is processed
* Age: \>= 18 years
* Karnofsky Performance Status (KPS) \>= 70
* Life expectancy \>= 16 weeks at the time of enrollment
* Patients requiring treatment for relapsed or refractory intermediate or high-grade B cell NHL (e.g., diffuse large B-cell lymphoma \[DLBCL\], mantle cell lymphoma \[MCL\], or transformed NHL) who are not eligible for, or who refuse, or have previously received autologous hematopoietic cell transplantation (autoHCT)

  * Note: COH pathology review should confirm that research participant's diagnostic material is consistent with history of intermediate or high-grade CD19+ malignancy
* No known contraindications to leukapheresis, lymphodepleting chemotherapy, steroids or tocilizumab, smallpox vaccine and any other MVA-based vaccines
* Patient must be CMV seropositive
* Total serum bilirubin =\< 2.0 mg/dL
* Participants with Gilbert syndrome may be included if their total bilirubin is =\< 3.0
* Aspartate aminotransferase (AST) \< 2.5 x upper limit of normal (ULN)
* Alanine aminotransferase (ALT) \< 2.5 x ULN
* Serum creatinine =\< 2.5 x ULN or estimated creatinine clearance of \>= 40 mL/min per the Cockcroft-Gault formula, and the participant is not on hemodialysis
* Absolute neutrophil count \>= 1000/uL (Transfusions and growth factors must not be used to meet these requirements at initial screening)
* Hemoglobin (Hb) \>= 8 g/dl (Transfusions and growth factors must not be used to meet these requirements at initial screening)
* Platelet count \>= 50,000/uL (\>= 30,000/uL if bone marrow plasma cells are \>= 50% of cellularity) (Transfusions and growth factors must not be used to meet these requirements at initial screening)
* Left ventricular ejection fraction \>= 45% within 8 weeks before enrollment
* Oxygen (O2) saturation \> 92% without requiring supplemental oxygen
* Women of childbearing potential (WOCBP): negative urine or serum pregnancy test

  * If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required
* Agreement by females and males of childbearing potential to use an effective method of birth control or abstain from heterosexual activity for the course of the study through at least 6 months after the last dose of protocol therapy

  * Childbearing potential defined as not being surgically sterilized (men and women) or have not been free from menses for \> 1 year (women only)

Exclusion Criteria:

* Prior allogeneic stem cell transplant unless the participant has recovered from transplantation and does not have active graft versus host disease (GVHD)
* Growth factors within 14 days of enrollment
* Platelet transfusions within 7 days of enrollment
* Concurrent use of systemic steroids or chronic use of immunosuppressant medications. Recent or current use of inhaled or topical steroids in standard doses is not exclusionary. Physiologic replacement of steroids (prednisone =\< 5 mg/day, or equivalent doses of other corticosteroids) is allowed
* Patients with active autoimmune disease requiring systemic immune suppressive therapy are not allowed
* Participants may not be receiving any other investigational agents or concurrent biological therapy, chemotherapy, or radiation therapy
* Any standard contraindications to lymphodepleting chemotherapy and/or CAR T-cell therapy per standard of care practices at COH
* Subjects with clinically significant arrhythmia or arrhythmias not stable on medical management within two weeks of screening
* Subjects with a known history or prior diagnosis of optic neuritis or other immunologic or inflammatory disease affecting the central nervous system (CNS), including seizure disorder, any measurable masses of CNS, or any other active CNS disease

  * Note: Research participants with a history of CNS disease that has been effectively treated to complete remission (\< 5 white blood cell \[WBC\]/mm\^3 and no blasts in cerebral spinal fluid \[CSF\]) will be eligible
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to study agents or cetuximab
* Known bleeding disorders (e.g., von Willebrand's disease) or hemophilia
* History of stroke or intracranial hemorrhage within 6 months prior to screening
* History of other malignancies, except for malignancy surgically resected (or treated with other modalities) with curative intent, basal cell carcinoma of the skin or localized squamous cell carcinoma of the skin; non-muscle invasive bladder cancer; malignancy treated with curative intent with no known active disease present for \>= 3 years
* Clinically significant uncontrolled illness
* Active infection requiring antibiotics
* Immunodeficiency virus (human immunodeficiency virus \[HIV\]) positive
* Active viral hepatitis
* Females only: Pregnant or breastfeeding
* Any other condition that would, in the investigator's judgment, contraindicate the subject's participation in the clinical study due to safety concerns with clinical study procedures
* Prospective participants who, in the opinion of the investigator, may not be able to comply with all study procedures (including compliance issues related to feasibility/logistics)