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Did you ever use it? I know that if you transferred it to a Gen 3 game while it's purified, you get a really good Psychic-type move (Psycho Boost!)..or, did you use it in X-D against Greevil to stall out his Shadow Pokemon?
I always use it against Greevil since by that point, my whole team is purified, therefore they're weak to shadow moves. Lugia just tanks it all, and the man has a full team of shadow Pokemon. I did purify it and send it to Emerald though, but it didn't get used much after that.
Like Syd said, I used Shadow Lugia during the late-game battles. I didn't have many shadow Pokemon on my team because they cannot gain levels. Shadow Lugia was the star of the team since it can take a hit and dish out damage.
I felt like Lugia wasn't nearly as interesting nor powerful once purified. When I eventually did that, it had a Bashful nature. I wanted something a little better, so in my second playthrough... I got a Bashful Lugia again. D: Screw that, let's just go to Navel Rock. :P caught a shiny Bashful Lugia