What do you mean? Are mouth shapes not moving correctly? Is your model bone driven or shape key driven? How did you key frame it and what kind of transition did you use?
Note that if you use shift-D to duplicate keyframes in the dopesheet editor, they are duplicated and linked to your mouse movement, so drag the mouse left/right on the timeline and you’ll should see the new keys. Also, and maybe this is what you were trying to do, because I just did it, just now, out of habit. In the dopesheet editor if you do a shift-D to duplicate, then follow with a shift-S to snap the key to the cursor, it won’t work. Move the key manually left/right with the mouse, then shift-S to snap to cursor.
How are you doing your lip sync? I view a phoneme graphic picture of the basic phonemes, create a pose library of the basic shapes of the mouth for each phoneme, then just insert the pose as I scan the timeline listening to the audio. Go thru the animation then a 2nd time adjusting controllers as need to fit the mood. If the character is yelling, open the mouth more, if whispering, close the mouth more.