Where do you get the thing to catch Lugia on HeartGold?

You can catch Lugia in Whirl Island in HeartGold.

Here's how to get there:

1. Beat the Elite Four and become the champion.

2. Talk to Professor Elm in New Bark Town. He'll tell you about the legendary birds.

3. Travel to the lighthouse on the east side of Ecruteak City. Use the Sea Skiff to reach Whirl Island.

4. Enter the cave on the island. You'll find Lugia at the end of the cave.

Important Note: Lugia is a level 70 Pokémon, so make sure you're well-prepared before encountering it.