Anchoring lip sync to tweened character face

Hello, I have no idea if this is a feature or how even to go about this.

I have a tweened head on one layer that moves from side to side. I have my mouth shapes for lip sync already drawn, but I can't find a way to have them follow the tween of the head without manually moving them frame by frame and hoping they stay in the same spot on the face. Is it possible to tween one mouth shape (ie. closed mouth) and somehow imput keyframes inside the tween that allows the mouth drawing to change, but the tween to follow its path? I also know theres an auto lip sync feature I've never used- is it possible to somehow tween one of these lip syncs and still have the mouth shapes change while continuing on their path? I am seriously lost as to how to impliment this practically. I appreciate any help ^^