My kitchen cabinets are 80's cabinets with a sticky lacquer on them.

Use a degreaser, I use Dollar Tree Awesome Degreaser, get the car sponge, kitchen rubber gloves, and round plastic scrubbies. I also start with the 1/2 gal of Awesome Orange in hot water and it gets 90% of it off, then I use the degreaser for the stubbord areas around the stove with a scrubby. Works everytime. If you fry/saute a lot grease aerializes onto the cabinets around your cooking stove and can be hard to get off without a degreaser. This works great as a pre-painting treatment too.

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

Gel stain is applied to the surface of the wood but not rubbed-in like traditional stains; the application is more comparable to painting on multiple thin layers. The gel stain is thick like pudding, not a liquid. While gel stain does go on thick and sit on the surface of the wood, I found that you can still see and feel the natural wood grain beneath, unlike paint. With the oak cabinets, the grain was very evident post-staining. Gel stain will not require you to sand the product to a raw wood finish. It can be applied over only lightly sanded pieces just as well. The condition of the wood does not play as big of a role in the finished result of the gel stain – the knots in your knotty pines will look less pronounced when the job is done. I found gel stain to be more forgiving; because you will need to do multiple coats, you can even out the finish over time. Because gel stain is thicker, it can be used for more creative applications too, like for painting a faux wood grain.

I agree with Sharon. A degreaser will clean them and remove the stickiness. Mineral spirits would also work. That's what I use.

Try sanding lightly and then wiping down with a liquid sandpaper to remove any film.

The grease has dissolved the finish. TSP is great. Have you cleaned the hood filter? Might be getting dangerous and catch fire. Clean all before painting, use Kilz to seal, then paint.

No mam the degreaser will not work. My cabinets are not nasty an greasy. The top cost of lacquer is coming off from the steam around the stove. Sanding them does not work either.

bottom is brown mahogany gel stain

Love this! This is kinda what mine look like at this point. I stripped the bottom cabinets with a strong commercial stripper. Then scrapped off the excess and gel stained them a walnut. They looked great but the hubs didn't like the dark? It was very time consuming to do the 10 cabinet doors and 5 drawers.

There are about 30 cabinet doors on the top cabinets. Thoughts on painting using a sprayer.

Use a good kitchen cleaner for grease and maybe wax removal. Then wipe them down with Surgical spirit. They should then be ok to paint.