Hmmm... If I am understanding correctly, you have engaged in a battle with Lugia and cannot seem to catch it, no matter how many Pokéballs you throw at it?
If so, how did you encounter Lugia? Did you actually visit a Nintendo Event to obtain the ticket required to enable access to Navel Rock, or are you using the aid of a hacking system such as a GameShark or an ActionReplay?
If you encountered Lugia on Navel Rock, I would assume that it isn't impossible to catch it, and that you are just having a difficult time catching it. If that is the case, you should be able to catch it, just keep trying.
If you encountered Lugia through means of a hacking system, the problem may be the codes you entered? I have almost no knowledge when it comes to hacking systems, so I cannot help much there.
However, may I also assume that you may be speaking of the Lugia from PKMN XD? If so, I believe that the Lugia must be caught with the Masterball (though I am unsure).
Anyone, feel free to correct me if any of the information I post is inaccurate/incorrect.
I hope this helps you,
~nguyende