In this study, researchers are assessing the safety and effectiveness of using the drug ruxolitinib in patients with T-cell lymphoma or natural killer (NK)-cell lymphoma that has come back or continued to grow despite prior treatment. Ruxolitinib is already approved for treating a bone marrow disease called myelofibrosis. It works by inhibiting a protein called JAK, which works with another protein called STAT to promote the growth of many T-cell and NK-cell lymphomas. By blocking JAK, ruxolitinib may cause lymphomas to shrink.