How can I fix the peeling lacquer clear coat on my kitchen cabinets?

Lightly sand it down and coat it again.

Yep! Sand and coat more than once (sanding lightly in between) I would use an oil based polyurethane instead of lacquer (unless you use several layers)

Make sure you use a compatible top coat, or you will have done everything for naught.

As a former antique furniture dealer I highly recommend Howards Restor a Finish. You can get it at Walmart and Amazon and it's about $8.00. Just follow the directions on the can and it's easy.

Agreed...Sand, stain and polyurethane. When your done do yourself a big favor and add hardware to your cabinets. Cabinets without them really take a beating.

You may find a few solutions on YouTube: https://www.youtube.com/results?search_query=how+to+repair+peeling+lacquer+on+kitchen+cabinets

Do a good job srip it and go to a good paint store to find out the best finish to reach the effect you want

New lacquer coats dissolve into previous coats so lacquer coats build up and become one thicker coat. Very light sanding and several coats of lacquer will solve the problem. Spray lacquer is ok if you can control the spray. Caution - Your lacquer may have yellowed if it is old so you may not get a perfect clear color match; might require very light stain on exposed wood to match. I would not use polyurethane over lacquer unless you sand/rough-up all surfaces to receive it. Polyurethane is a good product but it does not dissolve into the previous layer as lacquer does. Good Luck.

Another way is E.S.P. Easy Surface Prep. Paint it on and it eliminates sanding before resurfing cabinets.