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

* 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)

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)

What this study is about