The Geass-in-both-eyes thing is just how the ever-increasing strength of Lelouch's Geass manifests. C.C. mentions on multiple occasions that his Geass will grow stronger and stronger, to the point that it cannot be controlled (even by the special contact lenses).
I don't think there's anything to it beyond that. Lelouch's Geass seems to grow stronger precisely when the plot demands it - first it becomes always-on in one eye, triggering the Euphinator incident, and then it activates in both eyes, allowing him to get rid of Charles.