That is a good idea about the pressure washer and I have never seen it used. Another way to get rid of the lips (and requires much more work) is to rake it out in the offseason. Just grab some field rakes and rough it up and then use lawn rakes to pull back. I would much rather use the pressure washer.
Sometimes the way your field drainage / crown is set up will cause lips. For example the field I have played on for the past 10 years is elevated at the IF and slopes to the OF and foul sides. Because of this when water runs off the dirt goes with it towards the OF. So my lips were at the IF grass.
One thing we did was every so often (no real time table) was really tear up the dirt and take field rakes and flip them over so the flat side was touching the ground. Then push the dirt forward towards the IF grass. Basically you are taking the settled dirt in the back and moving it back where it used to be.
Another solution is to just bring in more dirt and level the areas.
To help lips form you can use brooms after each game and sweep the edge of the grass towards the dirt. This will move any loose dirt out of the grass and back onto the dirt.
Also when you drag don't take the drag up next to the grass. You want to stay about 10 inches to a foot away from the grass. You can rake or take the brooms to smooth that part out.