Just so it doesn't get lost, I want to lead with sports examples. The one that always comes to mind when the Pats are involved (frustratingly frequently) is the 'helmet catch' with which the Giants beat them. I understand, ala the discussion in another thread, that that play could well have been insignificant if a bunch of others hadn't gone the way they did. However, given the circumstances at the time, I find it really, really hard to believe that the Giants had a drill where they practiced grabbing a pass above their heads and pinning it against their helmet for a catch. And, I find it hard to believe that, if that scenario is repeated, the catch would be made. It was, IMO, a lucky catch.
Then, there are lucky breaks which have no bearing on your own preparation. If a placekicker, who prepares and practices to put the ball between the uprights, shanks one, and hits the upright, and it bounces through for the FG, that seems to be a lucky bounce. How about if Tom Brady trips coming on to the field for the SB - wouldn't that be a lucky break for the Eagles? Yes, they'd still have to play a good game that they prepared to do, but it would be a whole lot easier, due to an occurrence for which they didn't plan.
Now, the Steeler fumble in the Packer SB looks much more like preparation than luck. I still get goosebumps every time there's a replay of the game with Greene and Matthews just before the fumble - THAT was preparation meeting timing. Sure, the fumble might not have resulted, but there was obviously more than luck involved.
As to the lottery thing, what about a guy who wanders around looking for someplace to buy a six-pack, has a couple of bucks in change coming and figures 'what the heck?', buys the ticket, forgets about it, has a friend tell him the winning ticket was sold at the store where he bought his, rummages around his desk, finds the tickets, and...?