This phase Ib/II trial studies the side effects of acalabrutinib and duvelisib and how well they work in treating patients with indolent non-Hodgkin lymphoma that has come back (relapsed) or does not respond to treatment (refractory). Acalabrutinib inhibits a signaling molecule called Bruton tyrosine kinase and blocks cancer cell proliferation, growth, and survival. Duvelisib is designed to block a protein called PI3 kinase in order to stop cancer growth and cause changes in the immune system that may allow the immune system to better act against cancer cells. Giving acalabrutinib and duvelisib together may work better to block cancer growth than therapy of either drug alone.