Instructions
Acquire all eight Johto badges and head to New Bark Town. Speak with Professor Elm and he will present you with the Master Ball.
Fly to Ecruteak City and enter the Kimono House just north of the Pokemon Center. Defeat all five Kimono Sisters to get the Tide Bell.
Fly to Olivine City and surf south to reach the Whirl Islands. Use the HM move ̶0;Whirlpool̶1; to clear the whirlpools and enter the cave on the northeast island.
Make your way down the ladders to the bottom of the cave. Talk to the monk and he will allow you to pass.
Head south from the monk and enter the cavern where Lugia will appear.