Things You'll Need
Instructions
Go to docks at the southernmost point of Vermillion City.
Present the Mystery Ticket to the person at end of the dock. This will transport you to Navel Rock via the Seagallop Ferry.
Enter the cave at Navel Rock.
Walk to the right once you are inside the cave, and take the first ladder downwards.
Descend a series of five more ladders until you enter a room containing mostly water. Lugia will be sitting in the center of the room.
Engage Lugia in battle by walking up to it.
Battle Lugia until it has only a small amount of health remaining.
Throw a Poké Ball at Lugia to catch it.