The Lugia Chamber is located in the southwestern area of the Ruins of Alph. You'll need to progress through the Ruins to get to it, solving puzzles and avoiding the various traps.
Here's how to get to the Lugia Chamber:
1. Enter the Ruins of Alph from the east: You'll find the entrance near the Ecruteak City Pokémon Center.
2. Follow the path south and then west: There's a hidden path leading to the chamber, marked by a small opening.
3. Go through the opening and you'll enter the Lugia Chamber.
Note: You won't find Lapras in the Lugia Chamber. Lapras can be found in other areas of the game, like the Lake of Rage.