The study will consist of two stages. Stage 1 consists of a dose escalation stage to determine the MTD (or recommended dose based on available safety, PK and response data) using an accelerated titration scheme combined with standard dose escalation methods. GSK923295 will be administered intravenously over one hour, once weekly for 3 consecutive weeks (i.e., Day 1, 8, and 15) with treatment cycles repeated every 4 weeks (each cycle = 28 days). During Stage 1, safety, pharmacokinetics, pharmacodynamics, and clinical activity will be assessed. Tumor biopsies and PET imaging are optional in Stage 1 subjects. The MTD (or recommended dose based on available safety, PK and response data) will be defined as the dose of GSK923295 at which no more than 1 of 6 subjects experiences a DLT in the first treatment cycle. Eighteen subjects are anticipated to participate in Stage 1 of the study. In Stage 2, 15-20 additional subjects will be enrolled at the MTD (or recommended dose based on available safety, PK and response data) dose to further evaluate the safety of GSK923295. In Stage 2, PK samples (using a sparse PK sampling scheme for population PK analyses), PET imaging, and tumor biopsies will be obtained. Clinical activity will be assessed. Subjects (Stage 1 and Stage 2) will remain on study until they meet the criteria for treatment discontinuation described in the protocol. It is anticipated that 33-38 subjects will participate in the study (18 in Stage 1 and 15-20 in Stage 2. During Stage 1 and Stage 2, subjects with histologically confirmed advanced refractory solid tumors will be enrolled. In Stage 2, subjects with refractory non-Hodgkin's lymphoma and chronic lymphocytic leukemia can also be enrolled.