You find it in the Silver Trench after you've recruited the three legendary birds...But be careful, its a 99 floor dungeon with 6-7 one room monster houses(those are murder)
Lugia is in silver trench 99f size four ****
Lugia
fight lugia
You cant catch lugia on diamond and pearl but at red or blue rescue team in the silver trench
Silver trench 99f
You have to get ho_oh on your team then beat lugia with ho-oh then kill them again
you need to recruit zapdos moltres and articuno then talk to alkazam to gain acess to lugia
keep on beating it till it joins
after Befriending Lugia Meteor cave will open up.
You can get Lugia if you have a mystery part or a secret slab at the Surrounded Seas (I think 9th floor. I don't know for sure.)or if you are playing red rescue team or blue then recruit the 3 birds zaptose articUNO and moltres
you get it by entering meteor cave, which is found by blastoise the next morning after recruiting lugia
you find them on the floor in dungeons