Part A will follow a Continuous Reassessment Method (CRM) based on a Bayesian Adaptive Design to identify the AZD2014/ibrutinib dose combinations where the incidence of dose-limiting toxicity (DLT) is less than 33% during the first cycle. It is anticipated that approximately 30 evaluable patients with non-GCB DLBCL who are not eligible for stem cell transplant may be enrolled. The total number of patients, however, will depend upon the number of cohorts necessary to establish a tolerated combination dose. Determination of tolerated doses will be primarily based on the DLTs seen in Cycle 1. Each cycle will be 28 days. Part A will also include an assessment of single- and multiple-dose pharmacokinetics of the combination of AZD2014 and ibrutinib.