Can you remove it all the way to lath?

You would originally have had the plaster on lath.

Then someone went decorative and installed the sheets of linoleum-like material, perhaps to cover water damage or cracks, perhaps as a substitute for ceramic tile in places

Then a third layer - the drywall - was installed on top to cover the outdated stuff and maybe to conceal damage.

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The advantage of going all the way down to the lath is you can check for water damage to the studs, fix any lath problems, and install a good layer of water-resistant material under everything.

What are your plans for the bathroom? This will determine what you put on the walls.

It sounds like you're doing pretty close to a gut job, so if it were me, I'd take it down to the studs, clean it all out, and put greenboard/cement board back up. You'll gain a couple inches of room width that way, if you get rid of all the plaster.

There's not much point to keeping plaster that's covered up by something else.

I vote gut job. If you try to remove the linoleum I guarantee you'll damage the plaster, and have to remove it anyway-it's incredibly brittle. As old as it is it may already have lots of cracks. Just gut it to the lath, and drywall directly on that.