Now, this job depends on what tools you have and don't have. you will need a good jig saw, two counter top cutting blades. They must say for counter tops, they cut down ward instead of regular ones that cut up ward. This is to keep from chipping the counter top of the top surface.
Now, I take an extra precaution. Lay down several strips of blue painters tape. Not masking tape. Make the strips as wide as the sled of your jig saw, this is to prevent marring.
Now, with a felt tip pin, draw your lines showing how much of the lip to cut off. Do this on both sides.
Do your slow careful cuts blowing off the saw dust from your line so that your straight and smooth. Finish out one side then take a rest and procede to the other. then when done, take some light or fine grit sand paper and clean off your edges so the sharpness is dulled.