Laminate or wood floors are floating, meaning they are not nailed or glued. If you go this route, make sure the bottom of your doors have clearance.
Whatever you go with, needs to be under the toilet.
If you go with a peal and stick vinyl floor,, you can get the 3 foot x 4 inch tiles that look like real wood. In a house we remodeled a few years ago, we put laminate in the kitchen and used the vinyl in the master bed room. Unless the two were exactly side-by-side, you couldn't tell the difference until you actually stepped on them. Then the laminate had the wood "click" under your feet, and the vinyl and the rubber" click under your feet. Because they are tiles, they already had cracks between each one, which will aid in expansion and contraction over the changing seasonal temperatures.
You also have the option of going with carpet, or perhaps carpet over a section of the floor only that has the rip, put down a transition piece on the edge of the carpet and leave the rest original linoleum. If the torn area is not where a slide moved, this might be a good alternative, cheap, and will serve the purpose quite well. Now that the original linoleum already has the crack (for expansion) it probably will never crack anywhere else .... ever. So why not take advantage of it, and just cover the bad spot with carpet. You could try this, and if you don't like it, you can still pull up the carpet and the original linoleum and go to plan "B" ... whatever you think might work? If it were mine, I'd probably take this route.
Good luck!