 This phase II trial studies how well ixazomib citrate and rituximab work in treating patients with B-cell non-Hodgkin lymphoma that grows slowly indolent. Ixazomib citrate may stop the growth of cancer cells by blocking some of the enzymes needed for cell growth. Monoclonal antibodies, such as rituximab, may block cancer growth in different ways by targeting certain cells. Giving ixazomib citrate together with rituximab may work better in treating indolent B-cell non-Hodgkin lymphoma. 