IDK but that thing is fabulous! I can just imagine how terrific it's going to look when all spruced up!

Have you started cleaning them at all yet? I don't mean regular daily, I mean a serious deep clean. A gentle cleaner, especially if there is any grease there, is a mix of vinegar or lemon juice and water. Add a couple drops of dish soap. Inside and out. There are chemical cleaners meant for wood that you can use if the grunge wear isn't coming off with gentle cleaner.

Then from there depends a bit on how far you want to strip before refinish. You can go anywhere from full blown sanding down and complete refinishing.... to using denatured alcohol as a basic cleaning strip before moving on with prep for a refinishing oil or other sealant.

For that lip. If there are spots that are actively chipping or likely to let loose, I would address that and remove those spots. If they are already age smoothed then it's up to you if you want to sand them out more or not.

What do the insides look like? The outside looks like it's in great shape. Nice looking grain, glad it wasn't painted.

If the original finish is shellac, denatured alcohol will dissolve it. I'd recommend reapplying shellac as it's very DIY friendly. You can't screw it up; if you make a mistake, get out the denatured alcohol and begin again. Put a coat of paste wax over it and you've got a beautiful, hard, renewable finish.

I agree with Joseph.

I'd give josephs' approach a try. Use denatured alcohol on a small section or back of a door, see if it removes the top coat. Laquer thinner is another possibility. From there you'll need to use the back of the doors to experiment with a possible sanding schedule, dyes or gel stain that match that color, and a modern top coat. Once you've perfected the recipe, you can move on to the cabinet face.