Can micro liposuction get rid of my perioral mounds? (Photo)

These can be improved with a combination of fillers/fat, lasers, and skin tightening procedures.  Often chin implants or chin fillers can also help give improvement to the subpar jaw line and chin anatomy. Best, I recommend getting a formal evaluation with a facial sculpting expert. Dr. Emer.

This can be due to tissue laxity as you have suspected but there are cases where the fat pad of Bichet (lower facial fat pad) can actually herniate.  It can be treated by either intraoral removal if you desire a more hollow appearance here or it can be repaired.  In an MACS lift (minimal access cranial suspension) this fat pad is suspended and the excess skin removed from the front of the ear hidden in the sideburn and inside the ear canal.

This looks like ptotic buccal fat. If it is you should be able to milk it back up into position and remove it via a small incision inside the mouth. If it is ptotic buccal fat it makes no sense to inject a filler as camouflage.

Thank you for your question. I do not believe that liposuction will give you the improvement you are looking for and may make things worse by lowering the corners of your mouth or giving you additional hollowing of your cheeks. In fact, a bit of filler in the area or fat grafting may give you a much prettier result. Consult with an experienced board certified plastic surgeon to discuss minimal procedures that will accomplish minimal changes for you with minimal risk. Best of luck.

I don't think liposuction would help and could potential he make things worse.
It looks to me like if anything you have some loss of volume just behind the Area of concern.
For this I think you will definitely need an in person consultation to see what options could help.
Best,
Mats Hagstrom M.D.