you need the silver wing
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go to whirl islands
Summon Lugia with it at @ Whirl Islands Ancient Chamber
To find Lugia enter the Whirl Island Caves at the top-right island, then it should be pretty easy from there (if you're stuck use youtube or similar.)
there is no map. just use the pokegear. to get lugia you need to get a certain item first.
Go to whirl islands after defeating kimono girls and receiving silver wing..... ******note******* must know surf, flash, and whirlpool