You get a Pokemon that's effective against Phychic or Flying.
Personally, I wouldn't defeat Lugia...
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yes you can. but if you have Pokemon soulsilver, the first encounter will be a lugia and vice versa for ho-oh.
You can't unless you use gameshark
Lugia learns Sky Attack at level 99.
Once you defeat Lugia at the waterfall in the Whirl Islands, Lugia can no longer be obtained. Lugia does not appear anywhere else - only in that one place.
Lugia doesn't learn psychic in Pokemon soul silver on his own. However, you can easily teach Lugia psychic if you have the move in your possession.