You can only catch it with a gameshark.sorry
How To Find Lugia On Pokemon Leaf Green?
Or I keep hearing that there was an event for it but I'm not sure if they have it anymore
You go to pallet surf and wait for five minutes in the same spot you get 100 master balls and rare candies and then you go to brock and talk to him then lugia appears shiny at level 100 hp 999