Here are some projects on the subject:
This how-to-paint-your-linoleum-floors-yes/ link may be helpful.
Here’s a tutorial for you! https://realitydaydream.com/painting-linoleum-floors/
Don't ! I know it's a little more work but , it's well worth it..
The old comes up easier than you think. Take the molding
off around the corners of the floor. It may have so tacks
or staples in the corners. Then go to your home store
a talk to the flooring person. They will fix you right up.
It is some work but it is easy.
When you are done,,, WOW !!! You'll look back and say,
I did it my self !!!