Study to Evaluate Adverse Events, Change in Disease Activity, and How Intravenously Infused ABBV-291 Moves Through the Body in Adult Participants With Non-Hodgkin's Lymphoma

Inclusion Criteria: * For dose escalation (Part 1) only: Participants must have documented diagnosis of B-cell malignancies including (but not limited to) the following, with histology based on criteria established by the World Health Organization (WHO), and measurable disease requiring treatment: * Mantle cell lymphoma (MCL); * Marginal zone lymphoma (MZL); * Waldenstrom macroglobulinemia (WM); * Diffuse large b-cell lymphoma (DLBCL) (including: germinal center B-cell type, activated B-cell type, primary cutaneous DLBCL \[leg type\], Epstein-Barr virus-positive (EBV+) DLBCL \[not otherwise specified\], DLBCL associated with chronic inflammation, human herpesvirus 8-positive \[HHV8+\] DLBCL \[not otherwise specified\], B cell lymphoma \[unclassifiable\] with features intermediate between DLBCL and classical Hodgkin lymphoma, high-grade B-cell lymphoma \[not otherwise specified\], high-grade B-cell lymphoma \[with MYC (avian myelocytomatosis viral oncogene homolog) and BCL2 and/or BCL6 rearrangements\], DLBCL arising from follicular lymphoma \[FL\] \[transformed FL\]); * FL Grades 1 to 3B; * For dose expansion (Part 2) only: Participants must have documented diagnosis of one of the following B-cell malignancies, with histology based on criteria established by the WHO, and measurable disease requiring treatment: * Part 2a only: DLBCL (including: germinal center B-cell type, activated B-cell type, primary cutaneous DLBCL \[leg type\], EBV+ DLBCL \[not otherwise specified\], DLBCL associated with chronic inflammation, HHV8+ DLBCL \[not otherwise specified\], B-cell lymphoma \[unclassifiable\] with features intermediate between DLBCL and classical Hodgkin lymphoma, high-grade B-cell lymphoma \[not otherwise specified\], high-grade B-cell lymphoma \[with MYC and BCL2 and/or BCL6 rearrangements\], DLBCL arising from FL \[transformed FL\]); * Part 2b only: FL Grades 1 to 3B; * Part 2c only: Mantle cell lymphoma; * For all participants (Parts 1 and 2): * Must be considered relapsed or refractory to, or intolerant of, at least 2 or more prior lines of therapy known to provide a clinical benefit for their condition, and for whom there is no appropriate locally available therapy known to provide clinical benefit (e.g., standard chemotherapy or autologous stem cell transplantation \[ASCT\]). * Indolent non-Hodkin's lymphoma (NHL) participants must meet relevant disease specific requirements for treatment (e.g., National Comprehensive Cancer Network \[NCCN\], Groupe d'Etude des Lymphomes Folliculaires \[GELF\]). * History of allogeneic stem cell transplantation must be stable off of immunosuppression for at least 3 months. * For participants enrolled in backfill cohorts or at dose levels previously cleared, subjects must provide consent to an on-treatment fresh tumor biopsy from the same tumor lesion as the baseline tumor tissue. This requirement may be waived at the discretion of the contract research organization (CRO) Medical Monitor if collecting a biopsy would place the subject at risk of harm or would require a technically complicated procedure based on tumor location as assessed by the investigator or could hinder a subject's ability to participate in the study. * Previously treated with a CD79b-targeting therapy (e.g., CD79b monoclonal antibody) a core or excision tumor biopsy subsequent to the most recent CD79b-targeting therapy must be collected. Tumor biopsy requirements may be modified by Sponsor during the study. This requirement may be waived at the discretion of the contract research organization (CRO) Medical Monitor if collecting a biopsy would place the subject at risk of harm or would require a technically complicated procedure based on tumor location as assessed by the investigator or could hinder a subject's ability to participate in the study. * CD79b expression status will be assessed in all participants. * Have an eastern cooperative oncology group (ECOG) Performance Status of 0 or 1. * Laboratory values meeting the criteria in the protocol within the screening period prior to the first dose of study drug (if multiple samples are drawn within the screening period, the sample/result immediately prior to Cycle 1 Day 1 is applicable). * Availability of representative baseline tumor tissue (most recent archived tumor tissue or fresh biopsy collected during screening phase) suitable for immunohistochemistry (IHC) testing. This requirement may be waived at the discretion of the CRO Medical Monitor if collecting a biopsy at screening would place the participant at risk of harm or would require a technically complicated procedure based on tumor location as assessed by the investigator or could hinder a participant's ability to participate in the study. Exclusion Criteria: * History of interstitial lung disease (ILD) or pneumonitis that required treatment with systemic steroids, or any evidence of active ILD or pneumonitis. * Treatment with any of the following: * Anticancer therapy including chemotherapy, radiotherapy, small molecule, investigational, and biologic agents within 14 days (or at least 5 half-lives, whichever is shorter), prior to the first dose of the study treatment; * CD79b-directed agents (e.g., CD79b monoclonal antibody therapy) within 4 weeks (or at least 5 half-lives, whichever is shorter) prior to the first dose of study treatment. * Prior treatment with an antibody drug conjugate that consists of a topoisomerase I inhibitor.