There's no good reason to believe that Zuckerberg is lucky at all. Saying he was in the right place at the right time has this tacit assumption that if he were somewhere else at the wrong time he would have tried the same thing and fell flat on his face.
It seems because Facebook is an outlier, people feel safe talking about the luck factor, but that's meaningless because we all exist with individual circumstances, and by that measure everything every one of us does is based on luck. Instead, I prefer to ascribe luck to things that the individual actually had no control over, such as winning the lottery.