This phase II trial is studying how well giving rituximab together with combination chemotherapy and bortezomib works in treating patients with untreated mantle cell lymphoma. Monoclonal antibodies, such as rituximab, can block cancer growth in different ways. Some block the ability of cancer cells to grow and spread. Others find cancer cells and help kill them or carry cancer-killing substances to them. Drugs used in chemotherapy, such as cyclophosphamide, doxorubicin, vincristine, and dexamethasone, work in different ways to stop the growth of cancer cells, either by killing the cells or stopping them from dividing. Bortezomib may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Giving rituximab together with combination chemotherapy and bortezomib may kill more cancer cells.