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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.
Yeah, Lorelei (sp?) DOES have a Lapras, but she's referring to the scientist guy in the Silph Co. building that gives you one after you defeat Gary.
As for catching them in the wild, you can. After you beat the rockets in icefall cave, there is a slim chance of a Lapras appearing in that small pond.
Well, u can get a Lapras in 2 ways in FR/LG:
1) Get it after rival battle in silph co. building(same room as rival battle)
2) The room where u find Lorelei in Ice Cave on 4 Island. Surf There.(Very rare)
Hope that helped! ^^