A Study of AZD0486 Monotherapy or in Combination With Other Anti-Cancer Agents for Mature B-Cell Malignancies

Inclusion Criteria: 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. Exclusion Criteria: 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.