He's level 70 in Gold, and level 40 in Silver.
In Gold, you have to obtain the Silver Wing in Pewter City, which is accessible after you beat the E4.
Out of the four islands, I think you have to take the northeast one... Closer to Olivine City. And then follow that. Save in front of him, he's a sprite.
Use Ultra Balls. Try to avoid using ghost and dark moves.
REMEMBER: You need Surf, Whirlpool, Waterfall, and the Silver Wing in order to battle Lugia.
Avatar: In memory of ieatwyverns <3
Thank you, Vasco <3