This study focuses on individuals who have mantle cell lymphoma, which is a type of non-Hodgkin lymphoma. Zanubrutib is a drug approved by the U.S. Food and Drug Administration (FDA) for use in mantle cell lymphoma that has been previously treated. The purpose of the study is to evaluate the use of zanubrutinib in newly diagnosed mantle cell lymphoma that has not yet been treated. The study will compare continuous zanubritinib to treatment with zanubrutinib that is stopped after the initial six 28-day cycles of chemotherapy and restarted at the first time the patient’s disease worsens following the initial cycles of chemotherapy. The addition of zanubritinib to the usual treatment could shrink the patient’s cancer, but it may also cause side effects. Researchers aim to determine whether this approach is better, the same, or worse than the usual approach. The usual approach for patients who are not in a study is treatment with a combination of drugs approved by the U.S. Food and Drug Administration (FDA), including chemotherapy regimens that contain rituximab. Researchers will examine whether the study drugs increase the time to disease progression compared to the usual approach.