Does an underbite cause minimal improvement of a facelift?

Maybe. Assessing your profile, an experienced surgeon should be able to ascertain how your bone structure plays a role in your overall outcome. Loss of bone as we age is quite common an is exacerbated with age. There are alot of reasons for underwhelming results which can include not addressing deeper muscles as well.

You did not post photos, so I cannot be specific. if your underbite is fairly severe, it will interfere with your results.