Unfortunately, this is kind of a tricky issue, depending on what's driving your lip-sync in Unity. There are a couple ways of dealing with this, but the simplest (if it works for you) is probably to use the FBX export option to export a special blend shape that moves the jaw. It's called "Mouth Open as Morph".



If you export with that enabled, your model in Unity will have a new blend shape named "Merge_Open_Mouth". You can set up your lip sync software to also adjust this blend shape.
It's not perfect. A generally better approach is if your lip-sync software in Unity supports bone rotations in addition to simple blend shape manipulation, in which case you should just be rotating the jaw.