Once the plastic type top layer is up regular water will soften some of the paper middle.
depending on what floor covering is going to replace this you may not need to remove it all.
Replacing with Porcelin Tile Floors
I often set 1/4" backer right over the lino...with it screwed down. about 6" spaced screws on the edges and 8" in the field
Well it all depends on how it was put down. Some times it was just lied down and attach at the out side edge. This would make it easy to take up. But some times it was glued down and if yours was glued, then you have a bigger problem. The only way to get it up is to go rent a scrapper and scrap it up. And let me tell you that is a lot of work. And then you have to fill in all the uneven spots with floor leveler. So "KMS's" suggestion is by fare the fastest and the best way to cover glued Linoleum Flooring.