firstly, you must have the 8th badge,
you have to defeat team rocket in radio tower
you should get silver wing/rainbow wing from the REAL director
you should have go to Prof.Elm in New bark town and get a masterball
you should have surf(HM) and waterfall(HM)
You should have caught Raikou and Entei (released from burned tower)
You should have won the matches against the 5 kimono girl and get a bell(key item) =)( theres is 1 in icy path/cave but it doesnt matter)
if you have all those completed, go to whirls island =) go to the one that is the most north =)
there should be a monk at the bottom most lvl talk to him and he will activate the silver wing
go in to the bottom entrance(near the water surround by large rocks)
there should be the kimono girls standing in 1 straight line
talk to them and they will get the bell from you and the ritual will start.. after that Lugia will appear =)
Note this is a ONE chance fight... fail to catch it and you miss your chance.