This is a Phase 1b/2 study to investigate the safety and effectiveness of the investigational drug, cirmtuzumab (INN:zilovertamab), when given in combination with ibrutinib in patients with B-cell lymphoid malignancies. The Phase 1b will be conducted in two parts (Part 1 and Part 2). Part 1 is a dose-finding evaluation of the sequential administration of cirmtuzumab monotherapy followed by cirmtuzumab and ibrutinib combination therapy in chronic lymphocytic leukemia /small lymphocytic leukemia (CLL/SLL), previously treated mantle cell lymphoma (MCL) subjects that are BTKI naiive or have received a prior Bruton tyrosine kinase (BTK) inhibitor therapy, unless they demonstrated primary or acquired resistance to BTKi. Up to 48 subjects will be enrolled in Part 1 to determine the recommended dosing regimen (RDR). In Part 2, up to 60 subjects (CLL/SLL, MCL and MZL (marginal zone lymphoma) will be enrolled to further evaluate the safety and pharmacology of the cirmtuzumab and ibrutinib combination given at the RDR determined in Part 1 of the study. MZL subjects that have been previously treated and have relapsed after or progressed during at least one prior anti-CD20 -based therapy will be evaluated. In the Phase 2 (Part 3) portion of the study, approximately 30 subjects with CLL/SLL who may have received minimal prior BTK inhibitor therapy will be randomized to either Arm 1 (cirmtuzumab and ibrutinib) at the RDR or Arm 2 (ibrutinib alone) to evaluate the clinical activity and safety of the two arms.