Can paralysis of lower lip resolve?

After a facial nerve paralysis of the lower lip, you will need to give it time to heal spontaneously.  The deficit indicates a marginal mandibular nerve paralysis and these likely heal spontaneously but it will take months and not weeks.  There's a good chance it will heal in less than 6 months.  Be sure to follow with your surgeon and do not push for any quick intervention.

I would estimate this could take at least 3-6 months (possibly longer) to resolve, and certainly no potential interventions should be planned before this time (but of course stay in touch with your surgeon for reassessments as she sees fit . . . )

If there was no direct damage to the nerve and the paralysis was caused by stretching or swelling around the nerve, it could certainly resolve on it's own.  Have you seen any noticeable improvement in the 5 weeks since your surgery?  If so, that is a positive sign.  Unfortunately, I can't tell you how long.   It might be several weeks and possibly several months before it feels back to "normal".