This was taken from Pokémonaholic.com and I in no way wrote or know that this is correct but raven (the webmaster) tests most things she can. Anyways this is what I found when searching:
Go to the cave nearest to the city with the light house, or just follow the wall on the right-hand side while in the water. You will encounter two trainers and then a whirlpool. Use the whirlpool to get into the cave. Once inside, you will see a small walkway with jump-able bushes on one side. Jump over then go up and right. Go down the ladder. You will be on an island with an item nearby. Get the item and SURF down. Once down the waterfall, you will see an entrance in the cliff and a ladder. Go into the entrance. Then, Surf up to find Lugia, Use the ladder to exit the cave. Note: Lugia are at level 60 and are very hard to catch with any Pokeballs other than the Master Ball.
Hope this helps dude!
