The purpose of this study is to determine whether duvortuxizumab and ibrutinib can be combined safely and to establish the maximum tolerated dose (MTD) in Part 1 and the recommended Phase 2 dose (RP2D) and to further explore the safety of duvortuxizumab in combination with ibrutinib at the RP2D in participants with diffuse large B-cell lymphoma (DLBCL), follicular lymphoma (FL), mantle cell lymphoma (MCL), and chronic lymphocytic leukemia (CLL) in Part 2.