Lugia can be found and caught at the Navel Rock, one of the major sites of the Sevii Islands, in "Pokemon LeafGreen." Navel Rock is only accessible to players who have acquired a MysticTicket, an item that was handed out to attendees of Pokemon Rocks America.
With the MysticTicket at hand, players can ride a ferry at Seagallop Ferries and arrive at Navel Rock. Upon entering the destination, players must proceed to the right path to reach the lowest floor and encounter Lugia. The left path takes the players to the peak of Navel Rock, where Ho-Oh, another legendary Pokemon, can be captured.