Glofit and Obin in Follicular Lymphoma and Marginal Zone Lymphoma

Inclusion Criteria: * Histologically confirmed diagnosis of either FL (grade 1-3A) or MZL (any subtype) with review of the diagnostic pathology specimen at one of the participating institutions. Patients with active histologic transformation are excluded. * No prior systemic therapy for FL or MZL. Prior treatment with radiation therapy or short course steroids is allowed. * Meets at least one criterion to begin treatment based on the modified GELF criteria: * Symptomatic adenopathy * Organ function impairment due to disease involvement, including cytopenias due to marrow involvement (WBC \<1.5x109/L; absolute neutrophil count \[ANC\] \<1.0x109/L, Hgb \<10g/dL; or platelets \<100x109/L) * Constitutional symptoms * Maximum diameter of disease \> 7cm * \>3 nodal sites of involvement * Risk of local compressive symptoms * Splenomegaly (craniocaudal diameter \> 16cm on CT imaging) * Clinically significant pleural or peritoneal effusion * Leukemic phase (\>5x109/L circulating malignant cells) * Rapid generalized disease progression * Renal infiltration * Bone lesions * Patients cannot be in need of urgent cytoreductive chemotherapy in the opinion of the treating investigator. * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2. (Appendix A) * Age ≥18 years. * Adequate hematologic and organ function: * Absolute neutrophil count \> 1.0x109/L unless due to marrow involvement by lymphoma in which case ANC must be \>0.5x109/L * Platelets \> 75 x109/L, unless due to marrow involvement by lymphoma, in which case platelets must be \>50 x109/L * Creatinine clearance \> 40ml/min (by Cockcroft-Gault Formula) * Total bilirubin \< 1.5 X ULN, unless Gilbert syndrome, in which case direct bilirubin must be \< 1.5 x ULN * AST/ALT \< 2.5 X ULN, unless documented liver involvement by lymphoma, in which case AST/ALT must be \<5 x ULN * Ability to understand and the willingness to sign a written informed consent document. * Willingness to provide a pre-treatment tumor sample by core needle or excisional surgical biopsy. A fresh biopsy is strongly encouraged, but an archival sample is acceptable if the following provisions are met: 1) availability of a tumor-containing formalin-fixed, paraffin-embedded (FFPE) tissue block, 2) if the tumor containing FFPE tissue block cannot be provided in total, sections from this block should be provided that are freshly cut and mounted on positively-charged glass slides (SuperFrost Plus are recommended). Preferably, 25 slides should be provided; if not possible, a minimum of 15 slides is required. Exceptions to this criterion may be made with approval of the sponsor-investigator. * Willingness to remain abstinent or to use two effective contraceptive methods that result in a failure rate of \<1% per year from screening until: (a) at least 3 months after pre-treatment with obinutuzumab or 2 months after the last dose of glofitamab, whichever is longer, if the patient is a male or (b) until at least 18 months after pre-treatment with obinutuzumab or 2 months after the last dose of glofitamab, whichever is longer, if patient is a female. Examples of contraceptive methods with a failure rate of \<1% per year include: * Tubal ligation, male sterilization, hormonal implants, established proper use of hormonal contraceptives that inhibit ovulation, hormone-releasing intrauterine devices, and copper intrauterine devices. * Alternatively, two methods (e.g., two barrier methods such as a condom and a cervical cap) may be combined to achieve a failure rate of \<1% per year. Barrier methods must always be supplemented with the use of a spermicide. Exclusion Criteria: * Patients who require systemic immunosuppressive therapy for an ongoing medical condition will be excluded. For corticosteroids, patients receiving a prednisone dose of \>10 mg daily (or equivalent) will not be eligible. A short course of steroids (up to 14 days, not exceeding 40 mg dexamethasone or equivalent in a single day) for symptom palliation is allowed, in which case patients should be off steroids at least 7 days prior to treatment start. * Patients with bulky cervical adenopathy that is 1) compressing the upper airway or 2) in close proximity to the upper airway and could result in airway compression during a tumor flare event). * History of severe allergic or anaphylactic reactions to monoclonal antibody therapy unless in consultation with an allergy specialist they are deemed eligible for retreatment with desensitization. * Patients, who have had a major surgery or significant traumatic injury within 4 weeks of start of study drug, patients who have not recovered from the side effects of any major surgery (defined as requiring general anesthesia). * Patients with known HIV infection or hepatitis B or C infection. Testing for HIV is optional. Testing for hepatitis B and C is mandatory. Patients with hepatitis B core Ab positivity but negative surface antigen and negative viral load may be enrolled if they can be treated with a prophylactic agent (e.g., entecavir); patients with hepatitis C seropositivity who have a negative viral load can also be enrolled. * Patients with a systemic fungal, bacterial, viral, or other infection not controlled (defined as exhibiting ongoing signs/symptoms related to the infection and without improvement, despite appropriate antibiotics or other treatment). * Prior history of another malignancy (except for non-melanoma skin cancer or in situ cervical or breast cancer) unless disease free for at least 2 years. Patients with prostate cancer (Gleason score 6-7) are allowed if PSA is less than 1 ng/mL. * Patients should not have received immunization with lives or live attenuated vaccine within one week of study entry or during study period. * Patients who have any severe and/or uncontrolled medical conditions or other conditions that could affect their participation in the study or limit adherence to study requirements. * Patients with any one of the following currently on or in the previous 6 months will be excluded: myocardial infarction, congenital long QT syndrome, torsade de pointes, unstable angina, coronary/peripheral artery bypass graft, or cerebrovascular accident. * Patients with New York Heart Association Class III or IV heart failure. * Inability to comply with protocol mandated hospitalizations and restrictions * Patients who are pregnant, breast-feeding, or intending to become pregnant during the study. * Prior solid organ or allogeneic stem cell transplantation * History of known or suspected hemophagocytic lymphohistiocytosis (HLH). * History of autoimmune disease, including but not limited to myocarditis, pneumonitis, myasthenia gravis, myositis, autoimmune hepatitis, systemic lupus erythematosus, rheumatoid arthritis, inflammatory bowel disease, vascular thrombosis associated with antiphospholipid syndrome, Wegener's granulomatosis, Sjögren's syndrome, Guillain-Barré syndrome, multiple sclerosis, vasculitis, or glomerulonephritis • Patients with a remote history of, or well controlled, autoimmune disease may be eligible to enroll after consultation with the study PI.