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http://www.psypokes.com/forums/viewforum.php?f=51Anyway, I'm assuming that SoulSilver = Silver, so...
First off, get someone with False Swipe. Sycther learns it, so get him.
Now, get a pokémon with a Sleep Move. Let's say you have Butterfree.
It's not needed, but get a Pokémon with Dig, and Another with Fly.
Finally, get a pokémon that can NOT 1HKO Lugia, but still can shove off the majority of Lugia's HP. Let's say you have SudoWoodo.
Lead out with Sudowoodo and use Rock Slide.
Switch to Sycther and False Swipe like crazy
Sycther is probably dead if Lugia uses an Aeroblast, so bring Butterfree.
Use Sleep Powder
Keep using Ultra Balls
If It wakes up, Use Sleep Powder AGAIN.
Keep using Ultra Balls
Once you have captured Lugia, use Dig, then Fly to a pokémon center.