Nowhere; Lugia is not available in Pokemon Platinum (unless you migrate it over from a GBA game, in which case it'll be in the Pal Park).
all you have to do is get a pokemon who has surf,and surf around big oceans near cities.
Get the HM Surf then teach it to a pokemon.
First you have to have surf and waterfall. then surf from sunnyshore city and get through victory road and your there.
you can find it behind the valley windworks, you need to surf on the river to get to it.
You can find an electrilizer behind the valley windworks by using surf
Use surf to find lugia, there might be a mountain.
What ever you're smoking to think you can surf on lava, I want some!
You get Surf from the elder of Celestic Town.
Surf is HM #3. :-)
just use surf on almost any part of ocean
Use surf by the valley windworks and go right. There you willl find it.
you can get it by going to fuego fireworks but you nedd surf monkey