My 1911 home's main bath has plaster walls with original tile scoring on the lower half. The plaster, while cracked in a few places,seems sound and still well-attached. I have stripped wallpaper (top) and layers of paint down to what seems to be either the bottom layer or aged finish of the plaster--I can't tell. Where there was once a stove that layer seems heat-affected and a bit brittle:it chips in places (just one wall). There are some places where the paint has been difficult to strip completely. I've though about covering the lower half with beadboard panel, but don't know if the plaster will hold it. I cannot afford to replace the plaster but have to do something to finish it all. I've been indecisive for 4 years over this! Any suggestions??

plaster and lath won't hold diddly.

but they are attached to studs, and the studs will hold the weight of any stocked fixture you want to install.

warping and potentially some inconsistent construction techniques could mean the studs are not the standard 16 inches apart centerline to centerline. studfinders usually won't penetrate plaster very well, and if they do, they can be tricked by the lathing.

in the area you are going to beadboard, you could be really sure by using a small drill like a 1/8 masonry bit to drill a test hole about an inch deep after measuring 16 inches over from the last stud. if a nail hits wood after you pull the bit out, mark a line above where you will place the beadboard to ID the stud, and keep going.

in any event, the beadboard should be installed with snake-stripes of construction adhesive and nails into the studs.

second issue... beadboard is wood. wood rots when moist. plaster walls in bathrooms have no insulation behind them, and are going to be cooler than the air, and will build moisture under the beadboard. if you are dead set on doing this, shellac or varnish the material until it dries shiny, and then mount it. varnish won't hold paint worth a darn where you want it to stay, so the face has to be sanded and hit with a good primer like Kilz or 1-2-3.

I'd retile it myself. the brittle wall should probably be either overcoated with drywall or replaced with drywall, and if it's exterior, insulate it and put an 8 mil plastic overlay over that to prevent moisture issues inside the wall.