Inclusion Criteria:
* Ability to understand, willing, and capable of signing a written informed consent document
* Age ≥ 18 years
* Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1
* Histologically confirmed FL, grades 1-3a
* Relapsed after or failed to respond to at least two prior lines of systemic therapy and had received prior treatment with an anti-CD20-directed therapy
* Prior treatment-related adverse events (AEs) must have recovered to grade ≤ 1 with the exception of alopecia and grade 2 peripheral neuropathy
* At least one bi-dimensionally measurable lesion (≥ 1.5 cm in its largest dimension for nodal lesions, or ≥ 1.0 cm in its largest dimension for extranodal lesions within 6 weeks of screening by PET/CT scans with diagnostic computed tomography \[CT\] scan. PET/magnetic resonance imaging \[MRI\] scans may be allowed only if they are approved by the principal investigator \[PI\])
* Aspartate aminotransferase and alanine aminotransferase ≤ 3 x the upper limit of normal (ULN)
* Total bilirubin ≤ 1.5 x ULN; or total bilirubin ≤ 3 x ULN in patients with documented liver involvement or in patients with a documented history of Gilbert syndrome
* Platelet count ≥ 75 000/mm\^3 without transfusion within 14 days prior to first dose of pirtobrutinib
* Absolute neutrophil count ≥ 1000/mm\^3 in the absence of growth factor support
* Total hemoglobin ≥ 10 g/dL without transfusion within 21 days prior to first dose of pirtobrutinib
* Patients who did not meet criteria for hematologic function because of extensive marrow involvement of non-Hodgkin lymphoma, splenic sequestration, and/or disease-related cytopenia (e.g., immune thrombocytopenia) could be enrolled into the study if they have platelet count ≥ 50,000/mm\^3, absolute neutrophil count ≥ 750/mm\^3, and hemoglobin ≥ 7.5 g/dL after discussion with and confirmation by the PI
* Activated partial thromboplastin time (or partial thromboplastin time) and prothrombin (or international normalized ratio) ≤ 1.5 ULN
* Estimated creatinine clearance (CL) ≥ 30 mL/min by Cockcroft-Gault formula: (140 - age) x body weight (kg) x 0.85 (if female) serum creatinine (mg/dl) x 72 or other institutional standard methods (e.g., based on nuclear medicine renal scan)
* Negative serum pregnancy test within 3 days of initiating pirto for women of childbearing potential (WOCBP), defined as following: menarche and who are not postmenopausal (and 2 years of non-therapy-induced amenorrhea) or surgically sterile
* Fertile male and WOCBP patients must be willing to use highly effective contraceptive methods from the initiation of study treatment, until at least 3 months after the last dose of mosun or at least one month after the last dose of pirto, whichever occurs last
Exclusion Criteria:
* Prior BTK inhibitor (BTKi) refractory disease defined as disease progression or recurrence during or within 6 months of prior BTKi therapy. If disease progression or recurrence occurs \> 6 months after patients are off BTKi (e.g., due to intolerance), it is not considered as BTKi refractoriness. Patients with prior BTKi exposure but not meeting the criteria of BTKi refractoriness can be enrolled in this trial
* Prior exposure to pirtobrutinib
* CD3 T-cell engager exposed disease. However, these patients may be eligible if they stay in remission for at least 24 months after the last treatment with CD3 T-cell engager and have histologically confirmed CD20 expression on lymphoma at relapse or progression of disease
* Prior use of any monoclonal antibody, radioimmunoconjugate or antibody-drug conjugate within 4 weeks before first pirtobrutinib administration
* Prior treatment with systemic immunotherapeutic agents for which the mechanism of action involves T cells, including but not limited to cytokine therapy and anti-CTLA-4, anti-programmed death (PD)-1 and anti-PD-ligand 1 therapeutic antibodies, within 12 weeks or 5 half-lives of the drug, whichever was shorter, before first pirtobrutinib administration
* Treatment with any chemotherapeutic agent, or treatment with any other anti-cancer agent (investigational or otherwise) within 4 weeks or 5 half-lives of the drug, whichever was shorter, prior to first pirtobrutinib administration
* Treatment with radiotherapy within 2 weeks prior to the first pirtobrutinib administration. If patients received radiotherapy within 4 weeks prior to the first pirtobrutinib administration, patients must have had at least one measurable lesion outside of the radiation field. Patients who had only one measurable lesion that was previously irradiated but subsequently progressed are eligible
* History of allogeneic or autologous stem cell transplant (SCT) or chimeric antigen receptor-modified T cell (CAR-T) therapy within 60 days of enrollment or presence of any of the following, regardless of prior SCT and/or CAR-T therapy timing:
* Active graft versus host disease (GVHD);
* Cytopenia from incomplete blood cell count recovery post-transplant;
* Need for anti-cytokine therapy for toxicity from CAR-T therapy; residual symptoms of neurotoxicity \> grade 1 from CAR-T therapy;
* Ongoing immunosuppressive therapy (\> 20 mg prednisone or equivalent daily) or have been off immunosuppressive agents \< 2 months
* Prior solid organ transplantation
* Patients who cannot swallow oral medications
* History of bleeding diathesis
* Patients who experienced a major bleeding event on prior treatment with a BTKi
* Clinically significant active malabsorption syndrome or other condition likely to affect gastrointestinal absorption of the study drug
* 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 history of macrophage activation syndrome/hemophagocytic lymphohistiocytosis (HLH)
* Patients with history of confirmed progressive multifocal leukoencephalopathy
* History of severe allergic or anaphylactic reactions to monoclonal antibody or BTKi therapy
* History of other malignancy except for the following: history of second malignancy unless in remission for at least 2 years; in-situ carcinomas not requiring treatment intervention, non-melanoma skin cancer curatively treated, nonmetastatic breast, or nonmetastatic prostate cancer where hormonal therapy is being continued as standard of care are allowed
* Current or past history of central nervous system (CNS) lymphoma
* Current or past history of CNS disease, such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease. Patients with a history of stroke who had not experienced a stroke or transient ischemic attack in the past 2 years and had no residual neurologic deficits as judged by the investigator were allowed. Patients with a history of epilepsy who had no seizures in the past 2 years while not receiving any anti- epileptic medications were allowed in the expansion cohorts only
* Significant cardiovascular disease defined as:
* Unstable angina or acute coronary syndrome within the past 2 months prior to enrollment;
* History of myocardial infarction within 3 months prior to enrollment;
* Documented left ventricular ejection fraction (LVEF) by any method of ≤ 40% in the 12 months prior to enrollment;
* ≥ grade 3 New York Heart Association (NYHA) functional classification system of heart failure;
* Uncontrolled or symptomatic arrhythmias
* Significant active pulmonary disease (eg, bronchospasm and/or obstructive pulmonary disease)
* Known active and uncontrolled bacterial, viral, fungal, mycobacterial, parasitic, or other infection (excluding fungal infections of nail beds) at study enrollment, or any major episode of infection requiring treatment with IV antibiotics or hospitalization (relating to the completion of the course of antibiotics) within 4 weeks prior to first pirtobrutinib administration
* Known or suspected chronic active Epstein Barr virus infection
* Known active cytomegalovirus (CMV) infection. Unknown or negative status are eligible
* Recent major surgery within 4 weeks prior to first pirtobrutinib administration
* Known active hepatitis B virus (HBV) or hepatitis C virus (HCV) infection based on criteria below:
* Hepatitis B virus (HBV):
* Patients with positive hepatitis B surface antigen (HBsAg) are excluded
* Patients with positive hepatitis B core antibody (anti-HBc) and negative HBsAg require a negative hepatitis B polymerase chain reaction (PCR) evaluation before enrollment
* Patients who are HBV deoxyribonucleic acid (DNA) PCR positive will be excluded
* Hepatitis C virus (HCV): If positive hepatitis C antibody result, patient will need to have a negative result for hepatitis C ribonucleic acid (RNA) before enrollment. Patients who are hepatitis C RNA positive will be excluded
* Patients who have tested positive for human immunodeficiency virus (HIV) are excluded due to risk of opportunistic infections with both HIV and BTK inhibitors. For patients with unknown HIV status, HIV testing will be performed at Screening and result must be negative for enrollment
* Patients requiring therapeutic anticoagulation with warfarin or another vitamin K antagonist
* Pregnant or breast-feeding women
* Administration of live vaccination within 28 days of first administration of study drug
