Instructions
Insert a third-generation Pokemon game that has a Lugia in it in the GBA slot of your Nintendo DS.
Turn on the device and select Pokemon Platinum from the load screen.
Obtain the National Pokedex if you haven't already. The National Pokedex is rewarded to players that have encountered every Pokemon native to the Sinnoh region.
Fly to Route 221 and enter the Pal Park building.
Talk to the man behind the counter. He will ask you which Pokemon you want to transfer from the other Pokemon game in your device. Select Lugia.
Enter the park itself. Walk east to the water area, then north to the mountain area.
Walk around in the grass until Lugia appears. You will have to recapture it in a normal Pokemon battle.