This phase II trial studies how well obinutuzumab works in combination with ibrutinib in treating patients with mantle cell lymphoma that has returned (relapsed) or that does not respond to treatment (refractory). Obinutuzumab binds to a protein called cluster of differentiation (CD)20, which is found on B cells and some types of leukemia and lymphoma cells and help the immune system kill cancer cells. Ibrutinib blocks a protein called Bruton's tyrosine kinase (BTK), which may help keep cancer cells from growing. Giving obinutuzumab in combination with ibrutinib may kill more cancer cells.