This is only way I found to do it, and it still requires some cosmetic touch up and repair of the topcoat.
I remove the line tie, and then carefully use a bandsaw to cut a slot down the center of the broken lip, staying away from the actual surfaces where the lip is glued to the bait. I'm just trying to create some working space, not do a final removal.
Then I use a drywall knife (box cutter) to carefully pry the left over lip from the bait slot.
Once I get the old lip material out, I fit a new lip in, wedge it to the top surface to be sure it fits right, and then glue it in. I reinstall the line tie, and proceed with any cosmetic repairs and recoating.
It is slow and time consuming, and still requires lots of repairs prior to being able to fish the lure again.
I stopped doing it years ago because I'm lazy.