Can I redo my bathroom walls?

If you are asking whether you can remove the wallpaper then yes you can assuming that the plaster was primed or painted before the paper was applied. Do a test on an inconspicuous spot to make sure but you should have no problem. Our last house was plaster with several layers of wallpaper in nearly every room. It all came off eventually but the walls were fine.

you need to leave the laths up , but the plaster should go . This way you can see if your walls are insulated, if not then take down laths and install insulation. Nasty messy job be sure to close off the room or you will have dust everywhere! Good luck

Otherwise -Just Paper on top...........

Not sure if you're wanting to remove the wallpaper so you can paint or re-wallpaper but there's some "testing" you can do. First, I wouldn't take down all the plaster just to see if your walls are insulated. Your interior walls don't need to have insulation so that worry is only with exterior walls. Plus I'd leave that as a last resort as it is messy. If you have to remove the plaster I'd definitely leave the lath up as it gives good structure for future picture hanging. Some old wallpaper sticks pretty darn good but it comes off easily (both my front hallway and dining room had old - probably 60's - wallpaper and it came off like a dream). If you have an inconspicuous place (or it may not matter), use liquid fabric softener with the hottest water you can stand in a spray bottle. I think the ratio was 1/3 cup fabric softener to 2/3 cup hot water. If that doesn't work, there is a wallpaper product sold at Home Depot and Lowes. Some wallpaper isn't as porous as others (meaning the solution doesn't soak in good and loosen the paste/glue) but there is an item called a paper tiger that you rub over your wallpaper and it makes small holes in it for the solution to soak in. On our wallpaper it only took hot water to come loose so try that first. If the wallpaper is adhered permanently, is in good shape and is a smooth pattern, you might could prime and paint over it. Primer and paint formulas have improved so much and have much better coverage on non-normal surfaces than they used to (am I telling my age?) that I would check on that too. 1. Try stripping the wallpaper - hot water only first, hot water and fabric softener second, wallpaper stripper product third. 2. If none of that works and the wallpaper is smooth and in good condition, get small containers of primer and paint (or a good product with both of them combined) and try a small place to see if it works and you like it. 3. If neither of the first two options work, then I'd start removing the plaster. Youtube has some great videos of how to do this fairly easily. It is messy but you can handle that!

You can cover the wallpaper and your lath and plaster walls with wallboard if you wish. You'd be surprised what you can cover - including brick walls. Just make sure you are able to find the studs.