I have found Lugia in the cave I didn't go up and battle him and I was..

You can't get a second Master Ball unless you cheat. Try and use Dusk Balls to catch Lugia.

You can only get one MasterBall throughout the Game. If you want another one, you will have to get it by Trade or by an AR Code.

I would recommend you lower Lugia's HP as low as you possibly can. After that, make it fall asleep. Once that is done, throw Ultra Balls at it.

Hope this helps!

Personally I woud level you're team up a bit more preferably by 20 levels so you have a decent chance cause Lugia will b able 2 wipe you out almost right away he doesnt have alot of moves but they are powerful ones and will decimate you but as for the ball I wood use a regular pokeball or ultraball or great ball it's up to you but I wood save the ultra ball for one of the legendary dogs they are a pain in the arse 2 catch because you have 2 continiually attack and them nd they run away unless you have an arena trap or block or something along those lines I suggest you save the masterball for that umm as for where you get it I havnt played in so long but I beleive you after you beat clair you will get a call from prof elm telling you 2 stop by I think he will give it 2 you then or he will send you 2 erkratik city(no clue how 2 spell the darn thing) where you will have 2 fight all 5 of the kimona girls in a row you can't leave so make sure you pack a few full restores as well as a few revives they have all the eevee bunch and love stat effects (paralive burn such and such) and we all know the stat effects will hinder you're Pokemon well I hope I answered you're question oh and you should already have the masterball if you are looking at Lugia because you can't fight him until you go to the kanto region (if I'm correct)

You can win a second Master Ball at the lottery in Goldenrod (I won one once). You can also obtain more Master Balls by trading for them. However you can use any pokeball to catch any Pokemon.