Hmmmm.   I'd really like you to get an opinion from a dermtologist too.  Do you have a good one in your area?  Ideally, one who does the full range of medical, surgical and cosmetic dermatology.  When you say hypertrophic, I'm assuming they are small, whitish and raised since that's the kind of scar that usually occurs on the lips after electrocautery.  

Ask the dermatologist you see about doing a small "punch" excision of the scars.  Your lip would be numbed (much more comfortable), and a tiny, tiny instrument used to take out just the scar tissue, with 1-2 tiny stitches in for about 5 days.  This usually heals very nicely with no recurrence of the bump.   Your insurance may not cover this because it's cosmetic.   I'm not crazy about using Fraxel for this.  It would take many treatments to make much improvement in this type of scar on the lips.    Good luck!!!     Dr. I