VERY easy. All you have to do is eventually save or help the 5 Kimono girls, then battle all of them in the Ecruteak City Dance Theater. (They are fairly easy, because they each have only one Pokemon.) You must now have the Silver Wing and the Bell. Then, fly to Olivine City or Cianwood, surf to the islands, use Whirlpool, navigate Whirl Islands, find Lugia, and catch him. I used a Masterball. They never fail. Hope this helps!
First you will need to battle the five Kimono girls, then you will go to Cianwood City and surf to the right and use whirlpool where needed to go in the caves and follow the caves and you will find the Kimono girls again and they will let you battle Lugia, make sure you take strong pokemons and if possible put Luigia to sleep or paralyze it
You stock up on pokeballs, greatballs, and ultraballs. Then you go to the whirl islands after you get the silverfeather, and the tide bell. When you find lugia lowwer his life to almost zero and throw your ultraballs if you run out use your greatballs, if those run out, use your pokeballs and maybe confuse lugia and make him fall asleep even.
