If I remember correctly:
1.) Go to the Whirl Pool island.
2.) Find the cave where Lugia hides.
3.) Get to the final room where a man will ask for the silver feather.
4.) If you present him with it, you shall enter
5.) You will start to head up to battle Lugia, but the Koimo Girls (Eeveelution sister) will come in.
6.) They will preform their song and dance, and then you can battle Lugia.
7.) Try/catch Lugia and Escape Rope/Dig out.
Yeah, if I remember correctly, this is basically the run-down... So yeah, Hope This Helps!