Go through Silver Trench, which has 99 floors, and battle him. You should have a certain type of item that makes you have a higher chance of Pokemon joining your team, but if you don't them try to battle him until you recruit him.
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
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 get it by entering meteor cave, which is found by blastoise the next morning after recruiting lugia
how do you evolve golbat in pokemon blue rescue team
Recruit all 3 birds - Articuno Zapdos Moltres then go to their friend place and the event will activate.
Silver trench 99f