The lactose operon regulation in Escherichia coli is a primary model of phenotypic switching, reminiscent of cell fate determination in higher organisms. Under conditions of bistability, an isogenic cell population partitions into two subpopulations, with the operon's genes turned on or remaining off. It is generally hypothesized that the final state of a cell depends solely on stochastic fluctuations of the network's protein concentrations, particularly on bursts of lactose permease expression. Nevertheless, the mechanisms underlying the cell switching decision are not fully understood. We designed a microfluidic system to follow the formation of a transiently bimodal population within growing microcolonies. The analysis of genealogy and cell history revealed the existence of pre-disposing factors for switching that are epigenetically inherited. Both the pre-induction expression stochasticity of the lactose operon repressor LacI and the cellular growth rate are predictive factors of the cell's response upon induction, with low LacI concentration and slow growth correlating with higher switching probability. Thus, stochasticity at the local level of the network and global physiology are synergistically involved in cell response determination.