Escaping Lyman continuum photons from galaxies likely reionized the intergalactic medium at redshifts $zgtrsim6$. However, the Lyman continuum is not directly observable at these redshifts and secondary indicators of Lyman continuum escape must be used to estimate the budget of ionizing photons. Observationally, at redshifts $zsim2-3$ where the Lyman continuum is observationally accessible, surveys have established that many objects that show appreciable Lyman continuum escape fractions $f_{esc}$ also show enhanced [OIII]/[OII] (O$_{32}$) emission line ratios. Here, we use radiative transfer analyses of cosmological zoom-in simulations of galaxy formation to study the physical connection between $f_{esc}$ and O$_{32}$. Like the observations, we find that the largest $f_{esc}$ values occur at elevated O$_{32}sim3-10$ and that the combination of high $f_{esc}$ and low O$_{32}$ is extremely rare. While high $f_{esc}$ and O$_{32}$ often are observable concurrently, the timescales of the physical origin for the processes are very different. Large O$_{32}$ values fluctuate on short ($sim$1 Myr) timescales during the Wolf-Rayet-powered phase after the formation of star clusters, while channels of low absorption are established over tens of megayears by collections of supernovae. We find that while there is no direct causal relation between $f_{esc}$ and O$_{32}$, high $f_{esc}$ most often occurs after continuous input from star formation-related feedback events that have corresponding excursions to large O$_{32}$ emission. These calculations are in agreement with interpretations of observations that large $f_{esc}$ tends to occur when O$_{32}$ is large, but large O$_{32}$ does not necessarily imply efficient Lyman continuum escape.
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