• Histopathologically confirmed diagnosis of NLPHL as confirmed by local pathologist's expert review.

‣ Untreated NLPHL: stage IB to IV according to Cotswolds. The proportion of patients with stages I or II treated with consolidative radiotherapy will be capped at 40%.

⁃ Previously treated NLPHL, any stage.

⁃ According to the treating physician, the patient should not be observed and needs therapy, notably because of B-symptoms (unexplained fever \[temperature \> 38 degrees Celsius (\> 100.4 degrees Fahrenheit)\], weight loss \[unexplained loss of \> 10 percent of body weight over the past six months\], or drenching night sweats), symptomatic nodal or extranodal disease, or patient preferences.

• Patients must have measurable disease according to the Lugano/Lymphoma Response to Immunomodulatory Therapy Criteria (LYRIC) classification.

• Age \>= 18 years. Because no dosing or adverse event (AE) data are currently available on the use of mosunetuzumab in patients \< 18 years of age, children are excluded from this study.

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

• Absolute neutrophil count \>= 1,000/mcL.

• Platelets \>= 100,000/mcL.

• Total bilirubin =\< 1.5 institutional upper limit of normal (ULN), except in patients with Gilbert's syndrome as defined by \> 80% unconjugated bilirubin.

• Aspartate aminotransferase (AST)(serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine transaminase (ALT)(serum glutamic-pyruvic transaminase \[SGPT\]) =\< 3 x institutional ULN.

• Glomerular filtration rate (GFR) \>= 40mL /min= GFR (mL/Min/1.73 m\^2) \* body surface area (BSA)/1.73.

• Human immunodeficiency virus-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial.

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

• Patients 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.

• Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial.

• Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better.

• The effects of mosunetuzumab on the developing human fetus are unknown. For this reason and because other therapeutic agents used in this trial are known to be teratogenic, women of childbearing potential and men must agree to use adequate contraception (hormonal and/or barrier method of birth control; abstinence) (both hormonal and barrier method of birth control are required for participants in Canada) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men and women treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 3 months after completion of mosunetuzumab administration and 12 months after completion of rituximab administration.

• Ability to understand and the willingness to sign a written informed consent document. Legally authorized representatives may sign and give informed consent on behalf of study participants.