Instructions
Complete the game to start the process. Only after finishing the game can you capture the three legendary birds needed to trigger Lugia's appearance. Walk back to Mt. Thunder, where you first battled Zapdos. Mt. Thunder is directly east of the Silent Chasm, in the middle of the continent. Climb to the peak to find Zapdos. Equip the "Friend Bow" to increase your chances of befriending him. Your lead Pokemon should commit the final blow.
Travel to Mt. Blaze, where you first met Moltres. Mt. Blaze is directly north of Lapis Cave, on the northeast side of the continent. Ascend to the peak to fight Moltres. Moltres is weak against Rock- and Water-type Pokemon. Get Moltres to join your group by letting your lead Pokemon score the final blow.
Travel to the Frosty Forest, which lies directly northwest of Mt. Blaze. Ascend to the fifth floor of the Frosty Forest dungeon to reach Articuno. Bring Fire-type Pokemon to help fight his strong ice and water attacks. Defeat him with your lead Pokemon to capture this last legendary bird.
Travel to Town Square and speak to Alakazam. He sends you to investigate a storm near Legendary Island, located in the bay on the west side of the continent. Go there to see a cutscene and gain access to the Silver Trench.
Make your way to the Silver Trench. Travel northeast of the Legendary Island. Walk up to the 99th floor of the dungeon, where Lugia awaits you.