In Canada (which I assume you were referring to, as you didn't specify a jurisdiction) this claim is currently in litigation, so there is no definitive answer as to whether AI generated music is copyrightable or not. The currently accepted definition of "originality" (as required by the Copyright Act) is that it must involve the claimed author's "skill and judgment". Whatever that may mean in the context of AI is currently left for the reader to decide.

Depend on jurisdiction and probably how AI much is generated. If you write the lyrics but generate the song you still have copyright to the lyrics and so on

Why is that? And who draws the line? If I use a synthesizer to generate music, does that count as AI generated?