So before the stay-at-home orders for this pandemic, I bought a bunch of vinyl flooring for both bathrooms. It is very thin, clicks together and requires no glue, and can be placed directly over the linoleum (the linoleum acts as an underlayment to protect the floor from the concrete underneath). It's also waterproof, which is perfect for bathrooms.
The process is actually fairly simple. The main thing I think I would do differently is buy knee pads. I bruised my knees pretty good by being on the floor for so long. I also ended up using a lot more tools than I thought I would. The main ones were a hammer (used to tap a sacrificial piece of vinyl into the boards to tighten up the joints after they clicked together), crowbar (pry up baseboards, and move tiles that were along the wall), miter saw, and jigsaw (to cut the pieces to fit). But I also used an oscillating multitool (to cut door trim so flooring would slide under it), a tile contour gauge (to get better fits around objects like toilet flanges and wall protrusions), pencil (to mark lines to cut), and a utility knife (to trim pieces that weren't quite right).
Something I had a hard time figuring out were the gaps. To allow for expansion and contraction, you should leave a 1/4-inch gap around the walls. This is fine when there are baseboards that will go over the top and cover the gaps (or a transition piece to the carpet), but along the tub and shower, or the floor by the mirror, it was trickier. I learned a tip from a YouTuber - only leave 1/8-inch gap on those sides (as long as the opposite side will have a gap), and caulk the 1/8-inch gap with white silicone caulk. Another lesson learned - for those same spots, make sure the tile is in as straight a line as possible, so your caulk line looks great. Mine is less than great.
Anyway, here are some pictures - first the master bathroom:
And the upstairs bathroom - I actually did the toilet area first on this one, which I'm glad I did. Made the rest of the floor easier.
Oh, one more thing on those floor transitions. They use easily bendable plastic anchors, so when you drill your holes, make sure they are the right size and perfectly straight. Then go slowly when attaching the transition piece and make sure the bolts go in straight, or they'll bend, and you'll have to redo the whole thing...like me.
The last step was to touch-up and re-caulk the baseboards - the top with white latex caulk, and the bottom against the floor with white silicone caulk. I made the mistake of using an inflexible caulk along the floors before, and the caulk all cracked in the wintertime and pulled away from the baseboards.
Anyway, hope you enjoy!