Lip incompetence (strain when trying to close lips) can be from a variety of factors including but probably not limited to things like vertical maxillary excess, bucked out front upper teeth, anterior open bite, short upper lip, recessive chin, protrusive chin, chin too long. Those factors can be in combination--like someone having more than one of them--or an isolated factor can be pinpointed.
A common culprit, whether it be isolated as key culprit or it be in combination with other factors, is the CHIN. It's due to the mentalis muscle (muscle that allows you to move lower lip upward) being in an inefficient orientation which in turn is due to orientation of the chin bone. Basically, mechanical efficency of the mentalis muscle being easily able to move the lower lip VERTICALLY upward has to do with the SHORTEST distance to do that. The strain--and is a type of MECHANICAL inefficency--has to do when movement of the lower lip verticaly upward has to travel a LONG distance. Long distances can be DIAGONAL orientations when the chin is either too far backwards or too far forwards or they can be when the chin is too vertically long. Hence the chin bone, via a type of genioplasty would have to be displaced/reoriented with reference/goal to increase the mechanical efficiency of the mentalis muscle. That is the basic CONCEPT.
With regard to chin surgeries, how to do-- like whether to do incision from inside mouth or below chin--is different issue.