Umbralisib and Rituximab as Initial Therapy for Patients With Follicular Lymphoma and Marginal Zone Lymphoma

Inclusion Criteria: * Participants must have histologically confirmed follicular lymphoma grade 1-3A or marginal zone lymphoma by WHO criteria. * Participants must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter \[LDi\] to be recorded for non-nodal lesions and short axis for nodal lesions) as ≥15 mm in LDi for nodal disease or \>10 mm in LDi for extranodal lesions. * Requires therapy based on: symptomatic disease, threatened end-organ dysfunction, compressive disease, cytopenias secondary to lymphoma, bulky disease (defined as any site ≥7 cm, or 3 or more sites ≥3cm), or steady progression. * For patients with follicular lymphoma: No prior systemic therapy for follicular lymphoma. Prior radiation to a single site of disease is allowed if completed at least 2 weeks prior to initiation of protocol therapy and there are additional sites of measurable disease outside of the radiation field. * For patients with marginal zone lymphoma: No prior systemic therapy for marginal zone lymphoma. Prior radiation or surgical resection is allowed if there are additional sites of measurable disease outside of the radiation field. Prior radiation must be completed at least 2 weeks prior to initiation of protocol therapy. Prior H. pylori eradication therapy is allowed. * Age \>18 years. * ECOG performance status ≤2 * Participants must have adequate organ function as defined below: * total bilirubin \<1.5 x institutional upper limit of normal (ULN) or \<3 x ULN if considered due to Gilbert's syndrome * AST(SGOT)/ALT(SGPT) ≤2.5 × institutional upper limit of normal * creatinine within normal institutional limits OR * creatinine clearance ≥30 mL/min for participants with creatinine levels above institutional normal. * Participants must have adequate marrow function as defined below (unless abnormalities are considered related to marrow involvement by lymphoma): * absolute neutrophil count ≥1,000/mcL (500/mcL is acceptable if due to marrow involvement by lymphoma) * platelets ≥70,000/mcL(30,000/mcL is acceptable if due to marrow involvement by lymphoma) * Female participants who are not of child-bearing potential and female participants of child-bearing potential who have a negative serum pregnancy test within 3 days prior to initial trial treatment. Female participants of child-bearing potential and all male partners, and male participants must consent to use a medically acceptable method of contraception throughout the study period and for a minimum of 1 year after the last dose of rituximab and for a minimum of 4 months after the last dose of umbralisib. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Participants who require immediate cytoreduction per the treating investigator. * For patients with H. pylori related gastric extranodal marginal zone lymphoma in the absence of t(11;18): Patient must have relapsed or refractory marginal zone lymphoma despite appropriate H. pylori eradication. * For patients with hepatitis C virus related marginal zone lymphoma: Patient must have relapsed or refractory marginal zone lymphoma despite appropriate treatment of hepatitis C virus infection. * Active systemic therapy for another malignancy within 2 years. Local/regional therapy with curative intent such as surgical resection or localized radiation is allowed if patient is deemed at low risk for recurrence by treating physician. * Malignancy within 3 years of study enrollment except for adequately treated basal, squamous cell carcinoma or non-melanomatous skin cancer, carcinoma in situ of the cervix, superficial bladder cancer not treated with intravesical chemotherapy or BCG within 6 months, localized prostate cancer and PSA \<1.0 mg/dL on 2 consecutive measurements at least 3 months apart with the most recent one being within 4 weeks of study entry. * Corticosteroid therapy (prednisone \>10 mg daily or equivalent) is not permitted within 7 days prior to study entry. Topical, or intra-articular or inhaled corticosteroids are permitted. * Prior allogeneic stem cell transplant. * Inflammatory bowel disease (such as Crohn's disease or ulcerative colitis) * Malabsorption syndromes * Irritable bowel syndrome with greater than 3 loose stools per day as a baseline. * Known central nervous system involvement by lymphoma. * Evidence of histological transformation to large cell lymphoma. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to umbralisib or rituximab. * Evidence of ongoing systemic bacterial, fungal or viral infection, except localized fungal infections of skin or nails. * Evidence of chronic active Hepatitis B (HBV, not including patients with prior hepatitis B vaccination; or positive serum Hepatitis B antibody) or chronic active Hepatitis C infection (HCV), active cytomegalovirus (CMV), or known history of HIV. If HBc antibody is positive, the patient must be evaluated for the presence of HBV DNA (by PCR). If HCV antibody is positive, the subject must be evaluated for the presence of HCV RNA by PCR. If the patient is CMV IgG or CMV IgM positive, the subject must be evaluated for the presence of CMV DNA by PCR. Patients with positive HBc antibody and negative HBV DNA via PCR are eligible, but prophylaxis with entecavir or lamivudine is recommended. Subjects who are CMV IgG or CMV IgM positive but who are CMV DNA negative by PCR are eligible, but antiviral prophylaxis should be considered per institutional protocol. * Any severe and/or uncontrolled medical conditions or other conditions that could affect participation in the study such as: * Symptomatic, or history of documented congestive heart failure (New York Heart Association functional classification III-IV \[see Appendix: NYHA Classifications\]) * Significant cardiovascular disease such as uncontrolled or symptomatic arrhythmias, CHF, or myocardial infarction within 6 months of enrollment. * Concomitant use of medication known to cause QT prolongation or torsades de pointes should be used with caution and at investigator discretion. * Poorly controlled or clinically significant atherosclerotic vascular disease including cerebrovascular accident (CVA), transient ischemic attack (TIA), symptomatic peripheral arterial disease, angioplasty, cardiac or vascular stenting within 6 months of enrollment. * Psychiatric illness/social situations that would limit compliance with study requirements * Known history of drug-induced liver injury, alcoholic liver disease, non-alcoholic steatohepatitis, primary biliary cirrhosis, ongoing extrahepatic obstruction caused by stones, cirrhosis of the liver. * Pregnant women are excluded from this study because rituximab is an agent with known potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with rituximab or umbralisib, breastfeeding should be discontinued if the mother is treated with rituximab or umbralisib. These potential risks may also apply to other agents used in this study.