​I had Ultherapy today and my smile is asymmetrical on my lower part of the lips. Is this normal?

It is possible that swelling could affect your smile, but I would say that there is probably a more likely explanation for your issue.  It is possible that the Ultherapy treatment affected a nerve which is on the lower part of the face, causing the asymmetrical smile.  This should be a completely temporary issue and resolve over time. 

What you're describing sounds like a temporary issue that should resolve itself within a few days. During your Ultherapy treatment, it's possible that your surgeon inadvertently treated a nerve. If you're still experience issues a few days from now, I would recommend speaking with the surgeon who performed the procedure and have the issue diagnosed in person.

You may felt more pain in that area where asymmetry occured and that should have been a clue to the treating provider that a nerve is being irritated. Having said that it should resolve within 6 weeks (at most). Read the Ultherapy book (see link below). 

Don't worry, there have been no long term side effects from Ultherapy. Having said that, it is a powerful treatment (that is why it works!) and is not meant to be used in some small areas on the face where a nerve may be close to the skin.  If a nerve is inadvertently treated it may be traumatized for a matter of days.  The nerve always recovers quickly and your results from your treatment will far outweigh the temporary situation. (I am assuming that no anesthesia injections were done in the area which could also traumatize a nerve temporarily)

This could be related to swelling or nerve inflammation; both of which are temporary.  If your treating doctor used a local anesthetic to numb the area, then, this is most likely an effect from the local which should resolve by day's end.