Can anyone enlighten me about the micro-liposuction procedure to the perioral mounds area at the corner of the mouth?

It depends what you are referring to because in this day and aga there are a lot of gimmicks that non board certified doctors are using to get business.  I highly recommend that you see a few board certified plastic surgeon to assess you and give you PROPER recommendations.  

lipo or micro is not performed to treat the general issue you describing.  I have treated the problems you are describing for past 20 years and I recommend a formal consult evaluation in person. 

Good Afternoon,
Liposculpture of a very small area like the oral commissure/perioral mounds is difficult, even if "microliposuction" is done. It is hard to specifically tell how much fatty tissue is present without a photograph. 
I would look into the use of Kybella (deoxycholic acid) injecions to the area. This is FDA approved to "dissolve" fat, especially in the neck/submental area. It is easy, safe and will get the job done without surgery. It may take two sessions four to six weeks apart...but it will dissolve the fat without an incision. Check it out!!

I avoid surgery in this area, because of the long-term outcomes. 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.

In a word, "Don't!" Why?1. Much of the time it's not even caused by excess fat, rather by a detachment of the skin from the deeper tissues.2. In cases where it is caused by fat, removal of the fat tends to produce laxity of the skin that is very difficult to correct. I have seen cases where the bulge is due to skin laxity that improves with facelifting, but that is usually not the case.My best advice for treatment of these perioral mounds is to think in terms of a nonsurgical correction.

it’s just not a common procedure so it will be difficult to find someone who performs it frequently in high volume. 
A lot of surgeons perform breast augmentation because it is an incredibly satisfying procedure with highly satisfied patients. Micro Lipo doesn’t have the same outcomes and therefore is not frequently performed. 

I think you nailed it when you said in your question it is rare to find a surgeon familiar with liposuction of the area. If it worked well we would all be doing it. No one tries it more than once because it results in a very unhappy patient. I hope you are not going to be one of those unhappy patients someone tries it on. 

The region you describe is unfortunately not an area amenable to liposuction or simple surgical excision. You have too many muscles of facial expression attaching in this region to risk damage. Best wishes,
Jon A Perlman M.D., FACSDiplomate, American Board of Plastic SurgeryMember, American Society for Aesthetic Plastic Surgery (ASAPS)Beverly Hills, California