This is an open-label (identity of study drug will be known to participant and study staff), multicenter (when more than one hospital or medical school team work on a medical research study), Phase 1b study. The purpose of this study is to see if duvortuxizumab in combination with ibrutinib is safe and useful for treating participants with B-cell malignancies. This study will be conducted in 2 parts: Part 1: Dose Optimization and Part 2: Dose Expansion. Part 1 will determine what dose of duvortuxizumab can be given safely with the standard dose of ibrutinib to participants with previously treated B-cell malignancies. Part 2 will look at how previously treated DLBCL, FL, MCL, and CLL participants respond to a safe dose of duvortuxizumab in combination with ibrutinib. Part 2 will also test whether the dose from Part 1 is an effective cancer therapy. The study consists of a Screening Phase, an ibrutinib Run-In Phase (Part 2 only), a combination (duvortuxizumab plus ibrutinib) Treatment Phase (Day 1, Cycle 1 and continues until the completion of the End-of-Treatment Visit), End-of-Treatment Visit (30 days (+7 days) after the last dose of study drug), and Post-treatment Follow-up Phase. The end of the study will be defined as 12 months after the last participant has received the first dose of study treatment. Participants' safety will be monitored throughout the study.