• Histologically proven CD19- and CD20-positive LBCL, including transformation from indolent lymphomas.

• Have disease that is refractory to or relapsed \<=12 months after the completion of first-line chemoimmunotherapy

• • Refractory disease defined as no complete response (CR) to first-line therapy; participants who are intolerant to first-line therapy are excluded

• Progressive disease (PD) as best response to first-line therapy

• Stable disease (SD) as best response after at least 4 cycles of first-line therapy (e.g., 4 cycles of R-CHOP)

• Partial response (PR) as best response after at least 6 cycles, and biopsy-proven residual disease or disease progression ≤ 12 months from completion of therapy

• • Relapsed disease defined as CR to first-line therapy followed by biopsy- proven disease relapse ≤ 12 months of completing first-line therapy.

• Participants must have received first-line therapy including:

‣ Anti-CD20 monoclonal antibody

⁃ An anthracycline containing chemotherapy regimen

• Age 18 or older

• Eastern Cooperative Oncology Group (ECOG) performance status of ≤2.

• Participants must be willing and able to comply with protocol-mandated hospitalization upon administration of the first dose of glofitamab.

• Adequate bone marrow, renal, hepatic, pulmonary, and cardiac function defined as:

‣ Absolute neutrophil count ≥ 1000/μL

⁃ Platelet count either ≥ 75,000/μL or \>50K if documented lymphomatous involvement of bone marrow

⁃ Absolute lymphocyte count ≥ 100/μL

⁃ Creatinine clearance (as estimated by Cockcroft Gault) ≥ 30 ml/min

⁃ Serum alanine aminotransferase and aspartate aminotransferase ≤ 2.5 upper limit of normal (ULN)

⁃ Total bilirubin ≤ 1.5 mg/dL, except in participants with Gilbert's syndrome

⁃ Cardiac ejection fraction ≥ 45%, no evidence of pericardial effusion (except trace or physiological) as determined by an echocardiogram (ECHO), and no clinically significant electrocardiogram (ECG) findings

⁃ No clinically significant pleural effusion

⁃ Baseline oxygen saturation \> 92% on room air

• At least 2 weeks must have elapsed since any prior systemic therapy at the time the participants is planned for leukapheresis.

• Toxicities due to prior therapy must be recovered to Grade 1 or less (except for clinically non-significant toxicities such as alopecia).

• No suspicion of central nervous system (CNS) involvement of lymphoma.

• Participants must be willing and able to comply with protocol-mandated hospitalization upon administration of the first dose of glofitamab and with axi-cel.

• For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated.

• Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load.

• Participants with treated secondary CNS lymphoma are eligible if follow-up brain imaging after CNS directed therapy shows no evidence of disease.

• Participants with malignancy ≤2 years, whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen.

• Participants should be without any active cardiac symptoms and an ejection fraction \>45%, and a clinical risk assessment of cardiac function be class 2B or better using the New York Heart Association Functional Classification.

• Females of childbearing potential must have a negative serum or urine 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).

• Participants must agree to either remain completely abstinent or to use two effective contraceptive methods that result in a failure rate of \< 1% per year from screening until at least 3 months after pre-treatment with obinutuzumab or 2 months after the last dose of glofitamab (whichever is longer) if the participants is a male. If the participant is a female, effective contraception should be used until at least 18 months after pre-treatment with obinutuzumab or 2 months after the last dose of glofitamab (whichever is longer).

• Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of cycle-6 (C6) of glofitamab administration, and must refrain from donating sperm during this same period.

• • Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control.

• Ability to understand and the willingness to sign a written informed consent document.

• Autoimmune disease:

‣ Participants with a history of autoimmune-related hypothyroidism on a stable dose of thyroid replacement hormone may be eligible for this study.

⁃ Participants with a history of disease-related immune thrombocytopenic purpura or autoimmune hemolytic anemia may be eligible for this study.

⁃ Participants with a history of Type I Diabetes Mellitus who are well controlled (defined as a screening hemoglobin A1c \< 8% and no urinary ketoacidosis) are eligible.

⁃ Participants with eczema, psoriasis, lichen simplex chronicus, or vitiligo with dermatologic manifestations only (e.g., patients with psoriatic arthritis are excluded) are eligible for the study provided all of following conditions are met:

• Rash must cover \< 10% of body surface area

• Disease is well controlled at baseline and requires only low- potency topical corticosteroids

• No occurrence of acute exacerbations of the underlying condition requiring methotrexate, retinoids, biologic agents, oral calcineurin inhibitors, or high potency oral corticosteroids within the previous 12 months

• Participants with a history of stroke who have not experienced a stroke or transient ischemic attack in the past 2 years and have no residual neurologic deficits, as judged by the investigator, are allowed