I paralyzed Lugia and then brought his hp down with by using discharge, once he was in the red I used flash repeatedly so it's accuracy fell and then kept tossing ultra balls till it was caught after maybe 16 of them being thrown.
Nice way to show him who's bossMasterball...
I fought him over and over again using my Ultras but it just never happened because my luck sucks. So instead of keeping it up I finally got frustrated and restarted so I could stuff him in my Masterball. Then I put him in a PC box by himself and told him he could sit there for the rest of the game and suck it.