Cell lineage tracking is a long-standing and unresolved problem in biology. Microfluidic technologies have the potential to address this problem, by virtue of their ability to manipulate and process single-cells in a rapid, controllable and efficient manner. Indeed, when coupled with traditional imaging approaches, microfluidic systems allow the experimentalist to follow single-cell divisions over time. Herein, we present a valve-based microfluidic system able to probe the decision-making processes of single-cells, by tracking their lineage over multiple generations. The system operates by trapping single-cells within growth chambers, allowing the trapped cells to grow and divide, isolating sister cells after a user-defined number of divisions and finally extracting them for downstream transcriptome analysis. The platform incorporates multiple cell manipulation operations, image processing-based automation for cell loading and growth monitoring, reagent addition and device washing. To demonstrate the efficacy of the microfluidic workflow, 6C2 (chicken erythroleukemia) and T2EC (primary chicken erythrocytic progenitors) cells are tracked inside the microfluidic device over two generations, with a cell viability rate in excess of 90%. Sister cells are successfully isolated after division and extracted within a 500 nL volume, which is compatible with downstream single-cell RNA sequencing analysis.