Potassium Iodine is another option since it decreases proliferation activities of fibroblasts. I am not sure if the silicone scar strip or potassium Iodine will work faster. I will use the silicone scar strip while I sleep and the potassium Iodine drops during the day.
Although the following information relates to a keloid scar, it might also relate to thickened lip skin since iodine has been shown to decrease fibroblasts.
"Potassium Iodide ( SSKI ). SSKI must be rubbed into the keloid at least twice daily (more applications offer even better results) for several months to more than a year, depending on the severity of the keloid. Be patient, because progress often isn’t obvious for 2-3 months.
Despite the somewhat lengthy treatment period, persistence pays off. Eventually, SSKI will diminish a keloid scar until it’s just an “ordinary” scar, flat to the skin surface again. At that point, the SSKI applications can be discontinued and the keloid won’t re-establish itself."
There are different brands to choose. Here is an example: