There are many reasons that can cause drooping lips, including a combination of high blood pressure and diabetes medications, a CVA or cerebrovascular accident, brain tumor, a mini-stroke, a micro-stroke, extreme anger, poisoning from metallic, chemical, bacterial contaminants, remnant pesticide poisoning, toxic face cream poisoning, etc.
Visit the doctor immediately.
Check to see if there are any tumors in the brain.
Check to see if high blood pressure and diabetes are the causes.
Try to find out if there is any poisoning from contaminants.
Check the dinnerware for lead paint coating, lead paint glazing, etc.
If the drooping lips feel rigid, one can try to relax the stiff and rigid lip muscles by placing a hot towel over the lips and let the heat of the hot water soften the muscles of the lips.
If the drooping is the result of taking a combination of medications, stop taking the damn medicine and find another less harmful way to control the condition without relying on that combination of medications.