Master Inclusion Criteria applicable to all substudies: - Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2. - Contraception use during treatment and at least 90 days after final dose. - Confirmed CD19 expression if prior anti-CD19 therapy. Substudy 1 Specific Inclusion Criteria: - Participants with CLL must require treatment according to the international workshop on Chronic Lymphocytic Leukemia (iwCLL) criteria. - SLL: at least 1 measurable site per Lugano. - Absolute lymphocytes <10,000. - Cohort 1A and 1C: at least 2 prior lines of systemic therapy for CLL/SLL. - Cohort 1B: at least 1 prior line of therapy and is bruton tyrosine kinase inhibitor (BTKi)-sensitive. Substudy 2 Specific Inclusion Criteria: - MCL diagnosis per WHO. - Clinical Stage II, III, or IV by Ann Arbor Classification. - At least 1 measurable site per Lugano. - ALC < 10,000. - Cohort 2A and 2C: Relapse or progressed after 2 or more lines of therapy including BTKi. Substudy 3 Specific Inclusion Criteria: - Large B-cell lymphoma per WHO 2022. - R/R B-NHL after at least 1 prior line of therapy. - International Prognostic Index (IPI) 2-5. - At least 1 measurable site as per Lugano. - Left ventricular ejection fraction (LVEF) >50%. - Contraception at least 90 days after last dose of AZD0486 or 4 months after last dose of vincristine, and 6 months after the last dose of cyclophosphamide, or doxorubicin.

Master Exclusion Criteria applicable to all substudies: - Central nervous system (CNS) lymphoma. - Surgery within 14 days of study drug. - Clinically significant cardiovascular (CV) disease. - Unresolved Grade >2 AEs from prior anticancer therapy (except alopecia or fatigue). - Any anticancer therapy within 5 half-lives or 21 days (whichever is shorter) prior to treatment. - Radiation therapy within 28 days. - Prior CAR T-cell therapy or autologous-haematopoietic stem cell transplant (HSCT) within 12 weeks or prior T-cell engager (TCE) within 8 weeks. - Prior Grade > 3 cytokine release syndrome (CRS) or immune effector cell-associated neurotoxicity syndrome (ICANS) event. - Prior allogeneic HSCT or solid organ transplantation within 24 weeks of starting Cycle 1 Day 1. Substudy 1 Specific Exclusion Criteria: - CLL transformation to more aggressive lymphoma. - Cohort 1B: bleeding diathesis, CYP3A inhibitor or inducer, history of ICH or stroke within 24 weeks, GI malabsorption, receiving vitamin K antagonist. Substudy 3 Specific Exclusion Criteria: - Mediastinal grey-zone lymphoma, Burkitt, Richter's transformation, primary effusion large B-cell lymphoma (LBCL). - Cumulative dose of anthracycline >150 mg/m2.