During in situ liquid-phase electron microscopy (LP-EM) observations, the application of different irradiation dose rates may considerably alter the chemistry of the studied solution and influence processes, in particular growth pathways. While many processes have been studied using LP-EM in the last decade, the extent of the influence of the electron beam is not always understood and comparisons with corresponding bulk experiments are lacking. Here, we employ the radiolytic oxidation of Ce3+ in aqueous solution as a model reaction for the in situ LP-EM study of the formation of CeO2 particles. We compare our findings to the results from our previous study where a larger volume of Ce3+ precursor solution was subjected to γ-irradiation. We systematically analyze the effects of the applied irradiation dose rates and the induced diffusion of Ce ions on the growth mechanisms and the morphology of ceria particles. Our results show that an eight orders of magnitude higher dose rate applied during homogeneous electron-radiation in LP-EM compared to the dose rate using gamma-radiation does not affect the CeO2 particle growth pathway despite the significant higher Ce3+ to Ce4+ oxidation rate. Moreover, in both cases highly ordered structures (mesocrystals) are formed. This finding is explained by the stepwise formation of ceria particles via an intermediate phase, a signature of non-classical crystallization. Furthermore, when irradiation is applied locally using LP scanning transmission electron microscopy (LP-STEM), the higher conversion rate induces Ce-ion concentration gradients affecting the CeO2 growth. The appearance of branched morphologies is associated with the change to diffusion limited growth.