Always try to use different Pokeballs to catch the legendaries, especially the Game's mascot. I have Heart Gold, but I knocked out Ho-oH during our first battle. I captured it later after beating the Elite Four, using the Master Ball (even through, it was at 1 HP, paralyzed, under the effects of Atraction and after 3 or 4 Flashes from my Hypno. But I got out of Dusk Balls and Ultra Balls).
As for Lugia, I came much more loaded (hundreds of pokeballs. Many types xD). Ended up catching it with Heavy Ball, but I was pretty afraid. Had only 5 more Heavy balls and then I would have to use Heal Balls. FUUUUU, that was close xD