How do you get across the lake of rage on heart gold?

You can't actually cross the Lake of Rage in HeartGold. It's a large, mostly empty body of water with only one island in the middle. There is no way to traverse the lake itself, and you can't reach the island either.

The only way to get to the island is by using Strength on the boulder blocking the path to the south of the lake. This will allow you to reach the island and encounter the Legendary Pokémon Entei, Raikou, or Suicune, depending on the version of HeartGold you are playing.

However, it's important to note that you cannot access the island until after you have defeated the Elite Four and become the Pokémon League Champion.

Let me know if you have any other questions about HeartGold!