This phase II trial studies how well ofatumumab in combination with cyclophosphamide, doxorubicin hydrochloride, vincristine sulfate, and dexamethasone alternating with ofatumumab in combination with cytarabine and methotrexate works in treating patients with newly diagnosed mantle cell lymphoma (MCL). Monoclonal antibodies, such as ofatumumab, may interfere with the ability of cancer cells to grow and spread. Drugs used in chemotherapy, such as cyclophosphamide, doxorubicin hydrochloride, vincristine sulfate, dexamethasone, cytarabine, and methotrexate, 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. Giving ofatumumab together with alternating regimens of combination chemotherapy may kill more cancer cells.