This phase Ib trial studies whether anti-CD19-chimeric antigen receptor (CAR) lentiviral vector-transduced autologous T cells (JCAR014) and durvalumab are safe in combination and can work together in treating patients with non-Hodgkin lymphoma that has returned after a period of improvement or has not responded to previous treatment. JCAR014 is made of patients' immune cells (T cells) that have a new gene added to them in a laboratory, which programs them to kill lymphoma cells. Durvalumab is a type of drug called a monoclonal antibody, targeted to PD-L1 that may help immune cells attack cancer cells more effectively and thus help JCAR014 work better.