Lugia can be found at Navel Rock in Pok?mon FireRed. Obtaining it requires the Mystic Ticket, an event item that is received either by attending a Nintendo event or as a Mystery Gift.
The Mystic Ticket is required to board the ship that takes the player out to Navel Rock. Once the ticket is in hand, the ship can be boarded by talking to the sailor in front of the Seagallop Ferries. Lugia is found inside of Navel Rock on the first floor. It is also possible to trade in Lugia from several other Pok?mon games or to hack the game code to place it in the player's Pok?dex.