How do I paint highly lacquered wood cabinets?

The first thing you need to do is sand the cabinets with a rough grit sandpaper such as a 60-grit. This will do things...1-Knock down the glaze, 2-give the paint something to adhere to.

You need to thoroughly clean off all grease and dust. Use a paint deglosser or sand lightly to remove the sheen. You can then apply a new color stain. After that apply at least 2 coats of varnish or varathane. I like the varathane because it has a diamond hard finish and does not discolor. You can purchase kits, about $100, which have everything in it that you need and gives very detailed instructions on how to. There is enough in the kit to do a lot of cabinets.

You would need to lightly sand to remove the gloss and take it from there.

How to Paint Cabinets

Make sure they are clean and dry. Remove the doors and hardware. Mark the doors and cabinets with tape where they go. Lightly sand the doors and cabinets to remove any gloss and roughen the surface for paint with 100 grit sandpaper or a green Scotch Brite pad.. Use a tack cloth or damp rag to remove dust after sanding. Prime with a stain blocking primer like KILZ. Acrylic or water base paints are low-fume and clean up easily with water. Alkyd or oil-based paints require good ventilation because the paint contains solvents that can irritate your lungs and make you feel sick. Alkyd options require mineral spirits for cleanup, but they provide a hard, durable paint finish. Whichever you use, buy the best-quality paint you can afford for a lasting kitchen cabinet finish. Seal with at least three coats with a water based polyurethane. Use a small foam roller and foam brush for a smooth finish.

Good step by step instructions: https://www.doityourself.com/stry/how-to-paint-over-lacquer-on-kitchen-cabinets