Siltuximab for the Prevention of CAR T Cell Related Cytokine Release Syndrome in Patients With CD19 Positive Non-Hodgkin Lymphoma

Inclusion Criteria:

* Written informed consent obtained to participate in the study and Health Insurance Portability and Accountability Act (HIPAA) authorization for release of personal health information
* Age \>= 18 years at the time of consent
* Diagnosis of non-Hodgkin lymphoma
* Eligible for standard of care CD19.CAR-T cell therapy including axicabtagene ciloleucel, tisagenlecleucel, brexucabtagene autoleucel and lisocabtagene maraleucel)
* Subjects with hepatitis B virus (HBV) can be included if on suppressive antiviral therapy and have no detectable viral load
* Subjects with hepatitis C virus (HCV) can be included if HCV ribonucleic acid (RNA) viral load is undetected
* Measurable disease of \> 1.5 cm in diameter and/or bone marrow involvement
* White blood cell count \>= 1.0 x 10\^9/L (obtained within 14 days prior to initiating study treatment)

  * Note: Hematology and other lab parameters that are =\< grade 2 BUT still meet criteria for study entry are allowed. Furthermore, changes in laboratory parameters during the study should not be considered adverse events unless they meet criteria for dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy
* Hemoglobin \>= 8.0 x 10\^9/L (obtained within 14 days prior to initiating study treatment)

  * Note: Hematology and other lab parameters that are =\< grade 2 BUT still meet criteria for study entry are allowed. Furthermore, changes in laboratory parameters during the study should not be considered adverse events unless they meet criteria for dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy
* Platelets \>= 50 x 10\^9/L (obtained within 14 days prior to initiating study treatment)

  * Note: Hematology and other lab parameters that are =\< grade 2 BUT still meet criteria for study entry are allowed. Furthermore, changes in laboratory parameters during the study should not be considered adverse events unless they meet criteria for dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy
* Creatinine =\< 2.0 x upper limit of normal (ULN) (obtained within 14 days prior to initiating study treatment)

  * Note: Hematology and other lab parameters that are =\< grade 2 BUT still meet criteria for study entry are allowed. Furthermore, changes in laboratory parameters during the study should not be considered adverse events unless they meet criteria for dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy
* Bilirubin =\< 2.0 × upper limit of normal (ULN). Subjects with Gilbert's syndrome may be enrolled despite a total bilirubin level \> 2.0 mg/dL if their conjugated bilirubin is =\< 2.0 × ULN) (obtained within 14 days prior to initiating study treatment)
* Aspartate aminotransferase (AST) =\< 3.0 × ULN (obtained within 14 days prior to initiating study treatment)

  * Note: Hematology and other lab parameters that are =\< grade 2 BUT still meet criteria for study entry are allowed. Furthermore, changes in laboratory parameters during the study should not be considered adverse events unless they meet criteria for dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy
* Alanine aminotransferase (ALT) =\< 3.0 × ULN (obtained within 14 days prior to initiating study treatment)

  * Note: Hematology and other lab parameters that are =\< grade 2 BUT still meet criteria for study entry are allowed. Furthermore, changes in laboratory parameters during the study should not be considered adverse events unless they meet criteria for dose modification(s) of study medication outlined by the protocol and/or worsen from baseline during therapy
* Females of childbearing potential must have a negative serum pregnancy test within 3 days prior to registration

  * NOTE: Females are considered of childbearing potential unless they are surgically sterile (have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or they are naturally postmenopausal for at least 12 consecutive months. Documentation of postmenopausal status must be provided
* Females of childbearing potential must be willing to abstain from heterosexual activity or to use 2 forms of effective methods of contraception from the time of informed consent until 12 months after treatment the last dose of siltuximab. The two contraception methods can be comprised of two barrier methods, or a barrier method plus a hormonal method or an intrauterine device that meets \< 1% failure rate for protection from pregnancy in the product label
* Male subjects with female partners must have had a prior vasectomy or agree to use an adequate method of contraception (i.e., double barrier method: condom plus spermicidal agent) starting with the first dose of study therapy through 12 months after the last dose of siltuximab
* Subjects with prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the experimental regimen are eligible for the trial
* Subject is willing and able to comply with study procedures based on the judgement of the investigator or protocol designee
* FOR SILTUXIMAB TREATMENT OF CRS/ICANS: Any subject with grade 1 ICANS lasting \> 12 hours
* FOR SILTUXIMAB TREATMENT OF CRS/ICANS: Any subject with grade \>= 2 CRS after CD19.CAR-T cell therapy
* FOR SILTUXIMAB TREATMENT OF CRS/ICANS: Any subject with grade \>= 2 CRS after CD19.CAR-T cell therapy with concurrent ICANS
* SECOND SILTUXIMAB TREATMENT DOSE FOR CRS/ICANS: Subjects meeting criteria for a treatment dose who have received a treatment dose and have no change in the CRS or ICANS grade after 12 hours

Exclusion Criteria:

* Subjects requiring daily corticosteroids at a dose \> 10mg of prednisone per day (orequivalent). Pulsed steroids for disease control are acceptable
* Subjects who are planned to receive prophylactic steroids for mitigating CRS/ICANS before, during, or after CD19.CAR-T infusion
* Active central nervous system or meningeal involvement by lymphoma. Subjects with symptoms of possible central nervous system (CNS) disease should undergo CNS workup with magnetic resonance imaging (MRI) brain and diagnostic lumbar puncture prior to enrollment on this study. Subjects with a history of CNS or meningeal involvement must be in a documented remission by cerebrospinal spinal fluid (CSF) evaluation and contrast-enhanced MRI imaging for at least 90 days prior to registration
* Patients with history of clinically relevant and active CNS pathology such as epilepsy, seizure disorders, paresis, aphasia, uncontrolled cerebrovascular disease, severe brain injuries, dementia and Parkinson's disease
* Human immunodeficiency virus (HIV) seropositivity
* Pregnant or breastfeeding (NOTE: breast milk cannot be stored for future use while the mother is being treated on study and lactating females must agree to not breastfeed while taking study drugs)
* Uncontrolled concomitant illness including, but not limited to, symptomatic congestive heart failure (New York Heart Association (NYHA) Class III or IV), unstable angina pectoris, myocardial infarction within 1 month prior to enrollment, uncontrolled cardiac arrhythmias, uncontrolled seizures, or severe non compensated hypertension (systolic blood pressure \>= 180mmHg or diastolic blood pressure \>= 120mmHg)
* FOR SILTUXIMAB TREATMENT OF CRS/ICANS: Subjects with CRS and no evidence of ICANS who require dexamethasone (or any steroid) due to severity of CRS as determined by the investigators
* FOR SILTUXIMAB TREATMENT OF CRS/ICANS: Prior history of a dose limiting toxicity (see section 6.5) due to siltuximab infusion according to National Cancer Institute (NCI)-Common Terminology Criteria for Adverse Events (CTCAE) criteria v5.0
* SECOND SILTUXIMAB TREATMENT DOSE FOR CRS/ICANS: Subjects with CRS and no evidence of ICANS who require dexamethasone (or any steroid) due to severity of CRS as determined by the investigators
* SECOND SILTUXIMAB TREATMENT DOSE FOR CRS/ICANS: Prior history of a dose limiting toxicity due to siltuximab infusion according to NCI-CTCAE criteria v5.0