The purpose of this study is to determine the putative recommended Phase 2 doses (RP2Ds) and optimal dose schedule(s) for JNJ-95566692 as a single agent (Arm A) and in combination with JNJ-87801493 (Arm B) (Part 1: Dose Escalation) and to further characterize the safety and clinical activity of JNJ-95566692 as a single agent (Arm A) and in combination with JNJ-87801493 (Arm B) at the putative RP2D(s) (Part 2: Dose Expansion).

Inclusion Criteria:

• B-cell non-Hodgkin lymphoid malignancies (NHL) according to World Health Organization (WHO) 2022 with relapsed or refractory disease and no other approved therapies available that would be more appropriate in the investigator's judgment. • Histologic documentation of the following large B-cell lymphomas: o diffuse large B-cell lymphoma not otherwise specified (NOS), T-cell/histiocyte-rich large B-cell lymphoma, o diffuse large B-cell lymphoma/high grade B-cell lymphoma with MYC and BCL2 rearrangements, o large B-cell lymphoma with IRF4 rearrangement, o high grade B-cell lymphoma with 11q aberrations, o Epstein-Barr virus (EBV)-positive diffuse large B-cell lymphoma, o diffuse large B-cell lymphoma associated with chronic inflammation, o primary large B-cell lymphoma of immune privileged sites, o primary cutaneous diffuse large B-cell lymphoma-leg type , o primary mediastinal large B-cell lymphoma, o high-grade B-cell lymphoma NOS, o transformations of indolent B-cell lymphoma (For US sites). • Participants must have received at least 2 prior lines of therapy including an αCD20 monoclonal antibody containing chemotherapy combination schedule. • Participants who have received at least one prior line of therapy but are not eligible or do not have access to standard second line therapies, such as chimeric antigen receptor (CAR)-T, will be allowed to enroll. • Other B-cell NHL may be enrolled based on emerging data in specific cohorts as stipulated by study evaluation team (SET)
• While on study treatment and for 3 months after the last dose of study treatment, a participant must: not breastfeed or become pregnant; not donate gametes (that is, eggs or sperm) or freeze for future use for the purposes of assisted reproduction; and wear an external condom
• Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1
• Participants must have measurable disease as defined by the disease criteria (Lugano criteria)
• Participants of childbearing potential must have a negative highly sensitive (for example, beta [β]-human chorionic gonadotropin) pregnancy test at screening and within 24 hours before the first dose of study treatment and agree to further pregnancy tests

Exclusion Criteria:

• Known active central nervous system involvement (CNS) or leptomeningeal involvement
• Prior solid-organ transplantation
• Malignancy diagnosis other than the disease under study within 1 year prior to the first dose of the study treatment; exceptions are squamous and basal cell carcinoma of the skin, carcinoma in situ of the cervix and any malignancy that is considered cured or has minimal risk of recurrence within 1 year of first dose of the study treatment in the opinion of both the investigator and sponsor's medical monitor
• Autoimmune or inflammatory disease requiring systemic steroids or other immunosuppressive agents (for example, methotrexate or tacrolimus) within 3 months prior to first dose of study treatment
• Toxicity from prior anticancer therapy that has not resolved to baseline levels or to Grade less than or equal to (<=) 1 (except alopecia, vitiligo, peripheral neuropathy, or Grade <=2 endocrinopathies that are stable on hormone replacement)

The data sharing policy of Johnson & Johnson Innovative Medicine is available at innovativemedicine.jnj.com/our-innovation/clinical-trials/transparency. As noted on this site, requests for access to the study data can be submitted through Yale Open Data Access (YODA) Project site at yoda.yale.edu