When the old man gives the Silver Wing in Ecruteak City, go to the WhirlPool Islands and go to the North-Western Entrance. You need the HM WhirlPool and Surf. Go ahead and go through the dungeon. At the very bottom, surf and you will find Lugia waiting for you. Make sure you have pokemon around level 35-40, and Full Restores, and Ultra or Heavy Balls. SAVE IN FRONT OF IT. Battle it. Go weaken, put to sleep and start throwing the balls until you capture it. If you defeat it, reset the game so you find yourself right back in front of Lugia. Repeat as needed.