A Study to Assess the Adverse Events, Change in Disease Activity, and How Intravenously Infused ABBV-319 Moves Through the Bodies of Adult Participants With Relapsed or Refractory (R/R) Diffuse Large B-cell Lymphoma (DLBCL), Follicular Lymphoma (FL), or Chronic Lymphocytic Leukemia (CLL)

B-cell Lymphoma is an aggressive and rare cancer of a type of immune cells (a white blood cell responsible for fighting infections). Follicular Lymphoma is a slow-growing type of non-Hodgkin lymphoma. Chronic lymphocytic leukemia (CLL) is the most common leukemia (cancer of blood cells). The purpose of this study is to assess the safety, tolerability, pharmacokinetics, and preliminary efficacy of ABBV-319 in adult participants in relapsed or refractory (R/R) diffuse large b-cell lymphoma (DLBCL), R/R follicular lymphoma (FL), or R/R CLL. Adverse events will be assessed. ABBV-319 is an investigational drug being developed for the treatment of R/R DLBCL, R/R FL, or R/R CLL. This study will include a dose escalation phase to determine the doses of ABBV-319 that will be used in the next phase and a dose expansion phase to determine the change in disease activity in participants with R/R DLBCL, R/R FL, and R/R CLL. Approximately 154 adult participants with R/R B cell lymphomas including R/R DLBCL, R/R FL, and R/R CLL will be enrolled in the study in sites world wide. In the Dose Escalation phase of the study participants will receive escalating intravenously infused doses of ABBV-319 in 21-day cycles, until the Phase 2 dose is determined. In the dose expansion phase of the study participants receive intravenously infused ABBV-319 in 21-day cycles. There may be higher treatment burden for participants in this trial compared to their standard of care. Participants will attend regular visits during the study at an approved institution (hospital or clinic). The effect of the treatment will be frequently checked by medical assessments, blood tests, questionnaires and side effects.

Inclusion Criteria: * For dose escalation (Part 1) only: Participants with documented diagnosis of B-cell malignancies including those with histology based on criteria established by the World Health Organization (WHO), and measurable disease requiring treatment, as per the protocol. * For the relapsed or refractory diffuse large b-cell lymphoma (DLBCL), follicular lymphoma (FL), and Chronic lymphocytic leukemia (CLL) dose expansion cohorts (Part 2) only: Participants with documented diagnosis of one of the B-cell malignancies noted in the protocol with histology based on criteria established by the WHO, and measurable disease requiring treatment, as per the protocol. * Laboratory values meeting the criteria noted in the protocol. * For participants previously treated with a CD19-targeting therapy (eg, CD19 monoclonal antibody) a core or excision tumor biopsy subsequent to the most recent CD19-targeting therapy must be collected. * Participant must have measurable disease, as defined by the 2014 Lugano Classification. Exclusion Criteria: * Known active central nervous system (CNS) disease, or primary CNS lymphoma. * Known active infection or clinically significant uncontrolled conditions as per the protocol. * Eastern Cooperative Oncology Group (ECOG) performance status \>= 2.