There is no such thing as the Shadow Luiga. To catch the Shiny Lugia though, you need to find the code.
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You can't. It is not available on Pokemon Platinum.
I'm not sure but I think you can't
You can't catch Lugia in Pokémon Pearl. You have to trade it from Pokémon SoulSilver or HeartGold. You can also migrate it from Pokémon Emerald, FireRed, LeafGreen or Pokémon XD
You can catch Larvitar at the Rock PokeSpot on Pokemon XD for the GameCube,You can trade it onto Sapphire after you've beated XD001 (Shadow Lugia)
You use block or mean look at a lengedary Pokemon and then make it asleep and weaken it. After that, it's pretty easy to catch it. If you wanna catch LUGIA then you weaken it, lure it to sleep, and then it's easy to catch. Pokeballs and ultraballs are good against legendarys.