Natalizumab for the Prevention of ICANS in Patients With Recurrent or Refractory Diffuse Large B-Cell Lymphoma or Mantle Cell Lymphoma Receiving CAR T-Cell Therapy

Inclusion Criteria: * Patient must be ≥ 18 years of age at the time of signing informed consent (ICF) * Patient must understand and voluntarily sign the ICF prior to conduct of any study-related assessments or procedures * Patient must be willing to adhere to the study visit schedule and other protocol requirements * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 * Patient must be eligible per institutional criteria for therapy with commercial axicabtagene ciloleucel or brexucabtagene autoleucel for treatment of relapsed or refractory diffuse large B-cell lymphoma or mantle cell lymphoma * Per institutional protocol: Females and males 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 (female) or 4 months (males with female partners of reproductive potential) after the cyclophosphamide infusion. The two contraception methods can consist of two barrier methods or a barrier method plus a hormonal method. Female participants must agree to inform their male partners that they must use the methods of birth control required by the protocol. The use of intrauterine devices is excluded due to the risk of infection or bleeding Exclusion Criteria: * Uncontrolled systemic fungal, bacterial, viral, or other infection despite appropriate antibiotics or treatment * Patients with infections controlled on antibiotics are not excluded * Prior history or current infection with John Cunningham (JC) virus * Active hepatitis B or C (latent hepatitis B will not be excluded), or HIV. Entecavir prophylaxis can be used for latent hepatitis B. Patients' viral load must be undetectable per quantitative polymerase chain reaction (PCR) and/or nucleic acid testing at screening * Bilirubin: ≥ 2.0 x upper limit of normal (ULN), unless attributed to Gilbert's Syndrome or to the patient's primary malignancy * Aspartate aminotransferase (AST): ≥ 5 x ULN, alanine aminotransferase (ALT): ≥ 5 x ULN * Active concurrent autoimmune disease requiring immunosuppressive therapy * Active central nervous system (CNS) lymphoma * Active clinically relevant central nervous system disease including but not limited to: * Seizures/epilepsy * Stroke within the past 12 months, or unstable neurologic deficits within the past 12 months * Cerebral edema * Aphasia * Severe brain injury * Cerebellar disease * Documented history of dementia by clinical diagnosis * Parkinson's disease * Psychosis * Pregnant or nursing females * History of or active progressive multifocal leukoencephalopathy (PML) * Prior history or active herpes encephalitis or meningitis infection * Current treatment with any other agents for prophylaxis of CRS or ICANS, including investigational agents. Use of antiseizure medications does not exclude patients * History of prior exposure to natalizumab due to risk of neutralizing antibody formation * History of hypersensitivity reaction to natalizumab or the formulation excipients * Consider adding: History of, or a concurrent, clinically significant illness, medical condition or laboratory abnormality that, in the investigator's opinion, could affect the conduct of the study