• Age ≥ 18 years at the time of signing the informed consent form.

• Have a life expectancy (in the opinion of the investigator) of at least 12 weeks.

• Eastern Cooperative Oncology Group (ECOG) performance status \< 2 (Karnofsky \> 60%).

• History of previously treated MCL meeting the following criteria: Relapsed after or failed to respond to at least one prior line of systemic therapy including anti-CD20 monoclonal antibody and alkylator-containing chemotherapy.

• At least one bi-dimensionally measurable nodal lesion ( \> 1.5 cm in its largest dimension by PET/CT scan), or at least one bi-dimensionally measurable extranodal lesion ( \> 1.0 cm in its largest dimension by PET/CT scan) and FDG-avid.

• Availability of leftover tissue from the time of progression for pathology confirmation and correlative studies. Note: Formalin fixed paraffin embedded blocks are preferred. If blocks are not available, 12-15 slides containing unstained, serial sections are acceptable.

• Hemoglobin ≥ 9 g/dL (Independent of transfusions and within 7 days prior to screening assessment).

• Absolute neutrophil count \>= 1.0 x 10\^9/L (Independent of growth factor support and within 7 days prior to screening assessment).

• Platelets ≥ 75 x 10\^9/L or \>= 50 x 10\^9/L if due to bone marrow involvement (Independent of transfusions and within 7 days prior to screening assessment, and independent of growth factor support and within 7 days prior to screening assessment). If the patient is cytopenic there should be no evidence of myelodysplasia orhypoplastic bone marrow.

• Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (or ≤ 3 x ULN for participants with Gilbert syndrome, or \<= 3 x ULN if due to underlying lymphoma).

• Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase (SGOT)) \<= 2.5 X institutional upper limit of normal.

• Alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase (SGPT)) \<= 2.5 X institutional upper limit of normal.

• Creatinine clearance \>= 50 mL/min (by Cockcroft-Gault formula).

• Activated partial thromboplastin time (aPTT) or partial thromboplastin time (PTT) \<= 1.5 x ULN.

• Prothrombin (PT) or (international normalized ratio (INR) \<= 1.5 x ULN.

• In women of childbearing potential, negative serum pregnancy test within 7 days prior to study treatment and either abstinence or use of highly effective contraception methods from the time of screening for at least 18 months after pre-treatment with obinutuzumab, 2 months after the final dose of glofitamab, 1 month after last dose of pirtobrutinib, 3 months after the final dose of tocilizumab (if applicable), whichever is longer. Women of childbearing potential should not donate oocytes for 1 month after last dose of pirtobrutinib.

• For men: agreement to remain abstinent or use contraceptive measures and agreement to refrain from donating sperm, with female partners of childbearing potential or pregnant female partners, men must remain abstinent or use a condom during the treatment period and for at least 3 months after pre-treatment with obinutuzumab, 2 months after the final dose of glofitamab, 28 days after last dose of pirtobrutinib, 3 months after the final dose of tocilizumab (if applicable), whichever is longer.

• Willing and capable of giving signed informed consent which includes compliance with the requirements and restrictions listed in the informed consent form (ICF) and in the protocol.

• Participants with prior treatment-related adverse events (AEs) must have recovered to grade \<= 1 with the exception of alopecia and grade 2 peripheral neuropathy.

• Participants must be able to swallow oral medications.

• Participants with positive hepatitis B core antibody (anti-HBc) and negative hepatitis B surface antigen (HBsAg) require a negative hepatitis B polymerase chain reaction (PCR) evaluation before initiating study treatment on cycle 1 day 1. Participants with positive anti-HBc antibody are required to receive prophylactic antiviral therapy with lamivudine, tenofovir, or entecavir for the duration of treatment and for at least 6 months following the end of study treatment. Hepatitis B PCR should be repeated as clinically indicated.

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