Quote Originally Posted by Ryllharu
Lulu on the other hand, was given the Geass because C.C. saw in him the conviction he had, and his desperate need for power (the dialog in the first episode says all this).

I don't honestly think it has anything to do with any past they may have had when Lulu was young. It was a spur of the moment thing. He saved her, she saw his hatred for Britannia, a goal apparently well in line with her own, and she felt it necessary to reward him with the power he needed to fulfill his wishes and her own.
Definitely wrong.

Even before Lelouch saved C.C. in the 1st episode, C.C. already felt that the one she had been waiting for has come (she actually says something like this even before Lelouch got in the truck.) Lelouch also saw a shadow (probably of C.C.) appearing on top of the crashed truck. It definitely has a deeper meaning than just gratitude for her being saved, or overlapping goals.

You should not forget, that C.C. did not decide to give geass to Lelouch AFTER she was shot (or in the spur of the moment), because the very reason she was shot was because she protected him (probably because she has already chosen him as her new partner).

As far as I know, C.C. doesnt have mind reading powers (since she actually asks Lelouch questions), so Lelouchs determination or goal would have been unknown to her before she gave him geass, which basically sinks the argument of that being her motivation.

The events that have happened in episode 1 strongly suggest that the previous meeting has a greater meaning than what you suggest. If they dont elaborate on this, it will prove to be a big plot hole, since all of the things I mentioned above would fall out of place.