This phase II trial investigates how well modified VR-CAP (bortezomib, rituximab, cyclophosphamide, doxorubicin hydrochloride, prednisone, and cytarabine hydrochloride) and acalabrutinib as first line therapy work in treating transplant-eligible patients with mantle cell lymphoma. Modified VR-CAP is a combination of drugs used as standard first line treatment for mantle cell lymphoma. Chemotherapy drugs, such as bortezomib, cyclophosphamide, doxorubicin hydrochloride, and cytarabine hydrochloride, work in different ways to stop the growth of cancer cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Rituximab is a monoclonal antibody that binds and depletes malignant B cells, by inducing immune responses and direct toxicity. Acalabrutinib blocks a key enzyme which is needed for malignant cell growth in mantle cell lymphoma. Combining modified VR-CAP and acalabrutinib as first line therapy may be more useful against mantle cell lymphoma compared to the usual treatment.