I agree with Dr Lee that the best treatment would start with a proper assessment of the cause of your perceived upper lip protrusions. There is actually minimal subcutaneous fat in the upper lips of most people, so removal of fats in that area is very uncommon. The teeth and underlying bone structure will make more of a difference usually.
As we age, bone resorption at the maxilla bone causes its retrusion and a reduction of your maxillary angle can make the upper lips look more protruding. From a minimally invasive point of view, appropriate soft tissue fillers can help support the area of bone loss and reduce the protruding appearance. A certified facial plastic surgeon can also help with implants or jaw correction surgery.
Hope this helps!