What you can do if the lip is made of plastic and depending on how big the part is, is heat up a small section say in the very middle to the point where it will melt and push the lip together. It will still stay together and retain it's shape and when it cools you can cut, shave, mold it into shape. Of course if you never have done this, I would try practicing on something else similar to get the hang of it.
It's almost like plastic welding but you are compressing the plastic together in itself which will extrude the extra to the sides but like I stated you can cut the extra stuff off and shape it to how you want it.