The purpose of this randomized, open-label study is to evaluate the safety and efficacy of denintuzumab mafodotin plus RICE (rituximab, ifosfamide, carboplatin, and etoposide) when compared to RICE alone in the treatment of patients with relapsed or refractory diffuse large B-cell lymphoma (DLBCL) or Grade 3b follicular lymphoma. Eligible patients must also be candidates for autologous stem cell transplant. Patients will be randomly assigned in a 1:1 ratio to receive 3 cycles of study treatment with either denintuzumab mafodotin + RICE or RICE alone. The study will assess whether there is a difference between the 2 groups in the side effects that are reported and the number of patients who achieve complete remission at the end of their study treatment.