Phase II Study of Pirtobrutinib, Rituximab (PR) in Previously Untreated Low and Intermediate Risk MCL (Mantle Cell Lymphoma) Patients

Inclusion Criteria: The study will enroll 50 previously untreated low and medium risk MCL patients. Estimated 3 patients per month at minimum for enrollment. 1. Age ≥ 18 years old 2. Pathology confirmed diagnosis of mantle cell lymphoma. CD20 positivity is needed. Cyclin D1 negative MCL are allowed after confirming the diagnosis of MCL from hem-path at MDACC. 3. Newly diagnosed MCL with no prior therapy for MCL (age \>= 18 years) • Low risk - Ki-67% (\<= 30%), no features of high-risk disease (see below in exclusion), largest tumor size \<= 3 cm. * Medium risk - Ki-67% (\<=50%), largest tumor size \<=5 cm, no features of high-risk disease (see below in exclusion) 4. Participants with preexisting well-controlled cardio-vascular comorbidities - participants on anticoagulants (excluding warfarin and vitamin K antagonists), antiplatelet, anti-hypertensive, prior ablation, anti-arrhythmia, prior arrhythmias, baseline EKG abnormalities and cardiology clearance are allowed. Ejection fraction \>=50% and cardiology evaluation may be needed. (Echo and EKG and cardiology consultation within 2 months prior to C1D1 are allowed). 5. Understand and voluntarily sign an IRB-approved informed consent form. 6. Participants may have at least 1 site of radiographically assessable disease (i.e., lymph node longest diameter \[LDi\] \>= 1.5 cm, not necessary for disease assessable by positron emission tomography \[PET\]/computerized tomography \[CT\], extra nodal site \>= 1.0 cm in LDi. But participants with isolated gastrointestinal, bone marrow or spleen only disease patients are allowed. 7. Eastern Cooperative Oncology Group (ECOG) performance status of 2 or less (See Appendix III). 8. Prothrombin time (or international normalized ratio) and partial thromboplastin time not to exceed 1.2 times the institutional upper limit of normal range (participants with an elevated prothrombin time and known lupus anticoagulant may be eligible for participation after consulting the study PI). 9A. Adequate BM function independent of growth factor or PRBC or platelet transfusion support (within 14 days of Screening assessment and criteria must be met on C1D1 without transfusion/G-CSF within 7 days of assessment, per local laboratory reference range at screening as follows: a. platelet count \>=75,000/mm3; b. absolute neutrophil count (ANC) \>= 1000/mm3 unless cytopenia is clearly due to marrow involvement from MCL c. total hemoglobin \>= 8 g/dL (without transfusion support within 2 weeks of screening); If any of the above-mentioned cytopenias (a-c) are present due to significant BM involvement, at least 30% BM involvement by MCL (requiring transfusion or granulocyte colony-stimulating factor \[G-CSF\] support) MCL patients may proceed with enrollment after discussion with the PI or Co-PI. Cytopenias may not be due to evidence of myelodysplastic syndrome (MDS) or hypoplastic BM. 9B. Adequate organ function as defined by the following laboratory values: a. Creatinine clearance. \>=30 mL/min (by Cockcroft-Gault method, APPENDIX I), b. Total bilirubin ≤ 1.5 × ULN or ≤ 3 × ULN with documented liver involvement and/or Gilbert's Disease or controlled immune hemolysis or considered an effect of regular blood transfusions. c. Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \<3 x ULN, or \< 5 x upper limit of normal if hepatic metastases are present. 10\. Projected life expectancy of \>12 weeks pertaining to lymphoma. 11. Female participants must be surgically sterile, postmenopausal (for at least 1 year), or have confirmed negative results for a pregnancy test at screening, on a serum sample obtained within 7 days prior to initiation of study treatment. 12\. Women of childbearing potential and men with female partners of childbearing potential must be willing to use a highly effective form of contraception for at least 1 month after the last dose of study treatment. Participant enrolled into the Pirtobrutinib+ rituximab study should use a highly effective form of contraception for 1 month after the last dose of Pirtobrutinib and 12 months after the last dose of rituximab, whichever time period is longer. Recommended methods of highly effective birth control are: 1. Combined estrogen and progestin containing hormonal contraception associated with inhibition of ovulation given orally, intravaginally, or transdermally 2. Progestin-only hormonal contraception associated with inhibition of ovulation given orally, by injection, or by implant 3. Intrauterine device (IUD) 4. Intrauterine hormone-releasing system (IUS) 5. Vasectomized partner 6. Sexual abstinence: considered a highly effective method only if defined as refraining from heterosexual intercourse during an entire period of risk associated with the study treatment. The reliability of sexual abstinence will be evaluated in relation to the duration of the study and to the usual lifestyles of the participant. 7. Female sterilization 8. Fallopian tube implants (if confirmed by hysterosalpingogram) 13. Oocyte donation is prohibited during the duration of participation on this protocol and for 1 month after the last dose of Pirtobrutinib. Exclusion Criteria: 1. Participants with central nervous system involvement with mantle cell lymphoma or with suspected or confirmed progressive multifocal leukoencephalopathy (PML) are excluded since those participants have very poor prognosis, need aggressive intensive chemoimmunotherapy and intrathecal chemotherapy along with BTK inhibitors and these participants would not be eligible for this study. 2. High risk MCL - any or all of the following (Blastoid/pleomorphic histology), High Ki-67 (\>50%), Bulky disease (nodes \>5 cm, spleen \>20 cm), lymphocytosis \>=50,000 cells/uL, TP53 mutated or del17p by FISH. Presence of MYC rearrangement positive by FISH or MYC, Bcl2 amplification, complex karyotype or high-risk biologic MIPI (with Ki-67%) 3. Major surgery within 4 weeks prior to registration 4. History of bl