Ghostwolf does not work on the final boss of The Dawnbreaker

Yes that's expected, the combat actions in The Dawnbreaker dungeon are used for flying (one of two places in the game where that is needed so far, the other being Tindral Sageswift in Dragonflight). So the default combat actions including casting Ghost Wolf are overridden.

Is there any way to make it work? Or do you just have to make a separate keybind?

A way to have ghost wolf and the flying work in combat? No, it has to pick one or the other it can't make a decision in combat.

If you just want ghost wolf and no flying you can set your own combat macro in the settings to cast ghost wolf in combat.

https://github.com/xod-wow/LiteMount/wiki/In-Combat-Actions

But note:

This does not work when activating LiteMount using a macro on an action bar, due to Blizzard preventing macros from calling other macros.