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!!