Study of Capivasertib in Relapsed or Refractory B-cell Non-Hodgkin Lymphoma

Inclusion Criteria: * Participants must be ≥ 18 years of age, at the time of signing the informed consent * Eastern Cooperative Oncology Group performance status ≤ 2 * Life expectancy \> 6 months * Female participants must not be breast-feeding and must have a negative pregnancy test (serum) prior to start of dosing Module 1 specific inclusion criteria: Additional Inclusion Criteria for Cohort 1A (R/R FL): 1. Histologically confirmed diagnosis of FL Grade 1, 2, or 3a as assessed by investigator or local pathologist 2. Current need for systemic treatment based on the Investigator's opinion 3. Relapsed, progressed or refractory (defined as failure to achieve at least a partial response \[PR\]) after at least 2 prior systemic lines of therapy (including anti-CD20 monoclonal antibody \[mAb\] and an alkylating agent) 4. Bi-dimensionally measurable disease on cross sectional imaging by computed tomography (CT) or magnetic resonance imaging (MRI) with at least one nodal lesion \> 1.5 cm in the long axis or at least one extranodal lesion \> 1 cm in long axis. Additional Inclusion Criteria for Cohort 1B (R/R MZL): 1. Histologically confirmed MZL including splenic, nodal, and extranodal subtypes as assessed by investigator or local pathologist 2. Current need for systemic treatment based on the Investigator's opinion 3. Relapsed, progressed or refractory (defined as failure to achieve at least a PR) after at least 2 prior systemic lines of therapy (including at least one anti-CD20mAb directed regimen either as monotherapy or as chemoimmunotherapy; Helicobacter pylori eradication and radiation therapy alone will not be considered a systemic treatment regimen) 4. Bi-dimensionally measurable disease on cross sectional imaging by CT or MRI with at least one nodal lesion \> 1.5 cm in the long axis or at least one extranodal lesion \> 1 cm in long axis Additional Inclusion Criteria for Cohort 1C (R/R MCL): 1. Histologically confirmed MCL, with documentation of monoclonal B cells that have a chromosome translocation t(11;14)(q13;q32) and/or overexpress cyclin D1, as assessed by investigator or local pathologist 2. Relapsed, progressed or refractory (defined as failure to achieve at least a PR) after at least 2 prior systemic lines of therapy 3. Participants must have received as prior therapies Prior regimens must have included: * BTK inhibitor and * Anti-CD20mAb therapy 4. Bi-dimensionally measurable disease on cross sectional imaging by CT or MRI with at least one nodal lesion \> 1.5 cm in the long axis or at least one extranodal lesion \> 1 cm in long axis Exclusion Criteria: * Prior malignancy (other than the disease under study), except for adequately treated basal cell or squamous cell skin cancer, in situ cancer, or other cancer from which the participant has been disease free for ≥ 2 years * With the exception of alopecia, any unresolved non-haematological toxicities from prior therapy ≥ Common Terminology Criteria for Adverse Events Grade 2 at the time of starting study treatment * Known medically apparent central nervous system lymphoma or leptomeningeal disease * Inadequate bone marrow reserve or organ function as demonstrated by any of the following laboratory values at screening: 1. Absolute neutrophil count \< 1.0 × 10\^9/L; \< 0.75 × 10\^9/L in participants with known bone marrow involvement of malignant disease 2. Platelets \< 75 × 10\^9/L; \< 50 × 10\^9/L in participants with known bone marrow involvement of malignant disease 3. Creatinine clearance \< 50 mL/min per the Cockcroft and Gault formula * Clinically significant abnormalities of glucose metabolism as participants with diabetes mellitus type I or diabetes mellitus type II requiring insulin treatment and Glycosylated haemoglobin ≥ 8.0% (63.9 mmol/mol) * Prior treatment with any of the following: 1. Any investigational agents or study drugs from a previous clinical study within 5 half lives or 2 weeks from the first dose of capivasertib in this study 2. Strong inhibitors or inducers of CYP3A4 within 2 weeks prior to the first dose of study treatment (3 weeks for St John's wort), or drugs that are sensitive to inhibition of CYP3A4 within 1 week prior to the first dose of study treatment 3. Prior allogenic Haematopoietic stem cell transplant (HSCT) within 6 months from the first dose of capivasertib (patients \> 6 months after allogenic HSCT are eligible in the absence of active graft-versus-host disease and concomitant immune suppressive therapy). Prior cellular therapies (eg, Chimeric antigen receptor T therapy) and/or autologous HSCT within 3 months from the first dose of capivasertib 4. Receipt of live, attenuated vaccine within 28 days before the first dose of study treatment(s) 5. Participants who, due to other medical conditions /prior history /concomitant medications are, in the investigator's opinion, at a risk of a venous thromboembolism (VTE) and are not willing to accept the VTE prophylaxis, will be excluded. The initiation of an adequate VTE prophylaxis will be based on treating physician risk/benefit assessment and in agreement with the local management guidelines Additional exclusion core criteria may apply, please refer to the protocol Module 1 specific exclusion criteria: 1. Follicular lymphoma grade 3B 2. Known transformation to aggressive lymphoma, eg, large cell lymphoma 3. Participants who, in the Investigator's opinion, require immediate cytoreductive therapy for disease control