In LeafGreen, you acquire a Lapras from one of the Scientists in the Silph Co. Building. You'll need a spare slot in your party to acquire it, if memory serves. I don't think you can catch any in the wild, on FR/LG, but I could be wrong.
As for winning them, you can't; they aren't in the Game Corner, and the guy just gives it you, in the Silph Co. Building, anyway.