Inclusion Criteria:  Age: ≥ 16 years of age with no upper age limit. (NOTE: the first three subjects on this trial must be ≥ 18 years of age.)  Histologically confirmed aggressive B-cell NHL including the following types defined by World Health Organization (WHO) 2008:  Diffuse Large B-Cell Lymphoma (DLBCL) not otherwise specified; T cell/histiocyte rich large B cell lymphoma; DLBCL associated with chronic inflammation; Epstein Barr Virus (EBV)+ DLBCL of the elderly; OR Primary mediastinal (thymic) large B cell lymphoma; OR Transformation to DLBCL will also be included. Subjects must not have signs or symptoms of CNS disease or detectable evidence of CNS disease on magnetic resonance imaging (MRI) at screening; subjects who have been previously treated for CNS disease, but have no evidence of disease at screening are eligible. Subjects must have progressed, had stable disease, or recurred after two lines of therapies including an anthracycline and an anti-CD20 monoclonal antibody. Must have evaluable or measurable disease according to the revised International Working Group (IWG) Response Criteria for Malignant Lymphoma;26 lesions that have been previously irradiated will be considered measurable only if progression has been documented following completion of radiation therapy. Subjects who have undergone autologous stem cell transplantation (SCT) with disease progression or relapse are eligible.  Subjects who have undergone allogeneic SCT will be eligible if, in addition to meeting other eligibility criteria, are:  At least 100 days post-transplant, Do not have graft versus host disease (GVHD) At least 14 days or 5 half-lives, whichever is shorter, must have elapsed since any prior systemic therapy (including radiation therapy) at the time the subject is planned for leukapheresis, except for systemic inhibitory/stimulatory immune checkpoint therapy, which requires 5 half-lives. At least 7 days must have elapsed since any prior steroid use (dexamethasone or prednisone) prior to apheresis. Physiological replacement doses are allowable with no washout period. Topical or inhaled steroids for localized GVHD is allowable. Peripheral blood CD3 count must be >0.15 x 10^6 cells/mL within 14 days prior to proceeding with apheresis. Toxicities from prior therapy must be stable and recovered to ≤ grade 1 (except for clinically non-significant toxicities such as alopecia). Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1, or Karnofsky ≥ 80%.  Adequate organ function as defined by:  Absolute neutrophil count (ANC) ≥ 750/μL. Platelet count ≥ 50,000/ μL. Renal: Creatinine ≤ 2 mg/dL OR creatinine clearance (as estimated by Cockcroft Gault equation) ≥ 60 mL/min. Hepatic: Serum alanine aminotransferase (ALT)/aspartate aminotransferase (AST) ≤ 2.5 upper limit of normal (ULN). Total bilirubin ≤ 1.5 mg/dL, except in subjects with Gilbert's syndrome where a bilirubin <3.0 will be acceptable. Cardiac: Ejection fraction ≥ 45%, no evidence of physiologically significant pericardial effusion as determined by an echocardiogram (ECHO), and no clinically significant electrocardiogram (ECG) findings. Pulmonary: No clinically significant pleural effusion.  1. Baseline oxygen saturation > 92% on room air and; 2. Pulmonary Function Test: Diffuse capacity of the lungs for carbon monoxide (DLCO), forced expiratory volume in one second (FEV1) and forced vital capacity (FVC) are all ≥50% of predicted by spirometry after correcting for hemoglobin.  13. Females of childbearing potential must have a negative serum pregnancy test (females who have undergone surgical sterilization or who have been postmenopausal for at least 2 years are not considered to be of childbearing potential).  14. Subjects of childbearing or child-fathering potential must be willing to practice birth control from the time of enrollment on this study and for four (4) months after receiving the preparative regimen; females of childbearing potential must have a negative pregnancy test.  15. Must be able to give informed consent; subjects unable to give informed consent will not be eligible for this study.  16. Be able to consent to long-term follow-up protocol (#20-0188).  Exclusion Criteria:  Subjects meeting any of the following criteria are not eligible for participation in the study.  Age < 16 years of age. Previous CAR T therapy (Phase 1 only). Signs or symptoms of active CNS disease or detectable evidence of CNS disease on MRI at the time of screening. Subjects who have been previously treated for CNS disease, but have no evidence of disease at screening are eligible. History of malignancy other than non-melanoma skin cancer or carcinoma in situ (e.g., cervix, bladder, breast) unless disease free for at least 3 years. Uncontrolled fungal, bacterial, viral, or other infection requiring antimicrobials for management; simple urinary tract infection (UTI) and uncomplicated bacterial pharyngitis are permitted if responding to active treatment. Known history of infection with human immunodeficiency virus (HIV) or hepatitis B (hepatitis B surface antigen [HBsAg] positive) or hepatitis C.  8. History of myocardial infarction, cardiac angioplasty or stenting, unstable angina, or other clinically significant cardiac disease within 12 months of enrollment or have cardiac atrial or cardiac ventricular lymphoma involvement.  9. Venous thrombosis or embolism not managed on a stable regimen of anticoagulation.  10. Any medical condition that in the judgement of the sponsor is likely to interfere with assessment of safety or efficacy of study treatment.  11. History of severe immediate hypersensitivity reaction to any of the agents used in this study.  12. Pregnancy (serum pregnancy test must be obtained at time of enrollment for females of childbearing potential and to be repeated 72 hours prior to lymphodepleting chemotherapy regimen); females who have undergone surgical sterilization or who have been postmenopausal for at least 2 years are not considered to be childbearing potential.  13. Lactating. 14. In the investigator's judgment, the subject is unlikely to complete all protocol required study visits or procedures, including follow up visits, or comply with the study requirements for participation.  15. May not have primary immunodeficiency or history of autoimmune disease (e.g., Crohn's Disease, rheumatoid arthritis, systemic lupus) resulting in end organ injury or requiring systemic immunosuppression/systemic disease modifying agents within the last 2 years.  16. Unwilling to participate in long-term follow-up protocol that is required if CAR T cell therapy is administered at CU-AMC (#20-0188).