I don't usually try to do this, as I don't really have the patience for it and because sometimes the legendary will KO my whole team eventually if I waste time throwing useless Pokéballs at it.
However, I did catch a Lugia in SoulSilver with a Luxury Ball. The weird thing is, this battle was probably the hardest I've ever had to catch a legendary. I thought I would get it with some Dusk Balls and Ultra Balls, but they ran out quickly enough. Then I started throwing any random Pokéballs I had, because of my lack of preparation had left me with only a few left. I literally gave up and was about to restart when I decided to throw my last Luxury Ball, and it worked. I was so excited, as after all the others had failed, Luxury Balls had saved me.