It took me about four tries to capture Lugia when I confronted it. The fourth try being the most successful of course. I had kept going with the same tactics I had kept in mind, which was lowering Lugia down to 1HP with False Swipes by my Scyther, placing it to sleep with my Poliwhirl's Hypnosis and then just throwing Ultra Balls until I caught it.
Well, this turned out to be more difficult than thought out, because Lugia kept haxing me with Critical Hits and actually hitting my Pokémon even though some of his moves were not at full accuracy. Luckily, it didn't take too long to capture it after I placed Gyarados up front, which wore Lugia down for the first set of the battle. This ended up saving me time, my Pokémon and items.
At the end, I caught it with an Ultra Ball. Sadly, it's a Brave Nature, which sucks. :\ Good thing, I have no real plans to use it though.