The purpose of this study is to find the best dose of the drug and measure the safety and efficacy of LY4152199 in participants with previously treated B-cell malignancies. Participants will have the option to continue taking LY4152199 until the study ends.

Inclusion Criteria:

• Must have a diagnosis of either follicular lymphoma or diffuse large B-cell lymphoma.

• Must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.

• Estimated life expectancy of greater than or equal to (≥)12 weeks as judged by the Investigator.

• Participants with select tumor types must have measurable or assessable disease as defined below:

  • Participants with lymphoma must have at least 1 bi-dimensionally measurable lesion or in the absence of measurable lymphadenopathy, documentation of bone marrow involvement.
  • Participants with Waldenstrom macroglobulinemia (WM) must have measurable disease, defined as the presence of serum IgM with a minimum IgM level of greater than (>)2 times (×) upper limit of normal (ULN) based on local laboratory testing.

• Must be able to comply with inpatient/outpatient treatment, laboratory monitoring, and required clinic visits for the duration of trial participation.

• Must have adequate organ function.

Phase 1 Dose Escalation (Cohort A) Participants - Must have histologically confirmed relapsed/refractory B-cell malignancy.

Phase 1 Dose Optimization (Cohort B) Participants

- Must have histologically confirmed relapsed/refractory diffuse large B-cell lymphoma (DLBCL) de novo or transformed from follicular lymphoma (FL).

Exclusion Criteria:

All Participants

• Known or suspected peripheral blood involvement by malignant cells with an absolute lymphocyte count of greater than or equal to (≥) 5000 cells per microliter (μL).
• Known or suspected central nervous system (CNS) involvement by systemic lymphoma.
• Current or history of CNS disease, such as stroke, epilepsy, CNS vasculitis, or neurodegenerative disease
• Any unresolved toxicities from prior therapy greater than National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE) version 5.0 Grade 2 at the time of starting trial treatment except for alopecia.
• Autologous stem cell transplantation within 100 days of this study for post autologous transplant individuals.
• Residual symptoms of neurotoxicity or cytopenias from prior chimeric antigen receptor T-cell therapy (CAR-T) or bispecifics. Exception: Cytopenia related to prior CAR-T or bispecifics allowed if they meet the adequate organ function criteria.
• Known or suspected history of macrophage activation syndrome or hemophagocytic lymphohistiocytosis (HLH).
• Active second malignancies, unless in remission, with life expectancy greater than 2 years with Sponsor approval.
• History of autoimmune disease
• Significant cardiovascular disease
• Active uncontrolled systemic bacterial, viral, fungal, or parasitic infection (except for fungal nail infection), or other clinically significant active disease process
• Vaccination with a live vaccine within 4 weeks prior to signing informed consent form (ICF).
• Have current or had a history of severe allergic or anaphylactic reactions to monoclonal antibody therapy (or recombinant antibody-related fusion proteins).
• Prior treatment with B-cell activating factor receptor (BAFF-R) directed therapies (e.g., monoclonal antibody, CAR-T or bispecific antibody).
• Pregnant and/or planning to breastfeed during the trial or within 90 days of the last dose of study intervention.
• Known hypersensitivity to any component or excipient of LY4152199.