Studying dynamical processes by transmission electron microscopy (TEM) requires considering the electron-irradiation history, including the instantaneous dose rate and the cumulative dose delivered to the sample. Here, we have exploited liquid-cell TEM to study the effects of the electron-irradiation history on the radiochemical growth of dendritic Au nanostructures. Besides the well-established direct link between the dose rate and the growth rate of the nanostructures, we demonstrate that the cumulative dose in the irradiated area can also induce important transitions in the growth mode of the nanostructures. By comparing in situ observations with an extended diffusion-limited aggregation model, we reveal how the shape of the nanostructures is severely affected by the local lack of metal precursors and the resulting restricted accessibility of gold atoms to the nanostructures. This study highlights the effects of electron irradiation on the solution chemistry in the irradiated area and in the whole liquid cell that are of primary importance to extract quantitative information on nanoscale processes.