This phase II trial is studying how well giving combination chemotherapy together with rituximab and bevacizumab works in treating older patients with stage II, stage III, or stage IV diffuse large B-cell lymphoma. Drugs used in chemotherapy work in different ways to stop the growth of cancer cells, either by killing the cells or by stopping them from dividing. Giving more than one drug (combination chemotherapy) may kill more cancer cells. Monoclonal antibodies, such as rituximab and bevacizumab, 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. Bevacizumab may also stop the growth of cancer cells by blocking blood flow to the cancer. Giving combination chemotherapy together with monoclonal antibodies may kill more cancer cells.