It sounds like this is not in the shower. The tile application you describe is an odd one. Older homes with tile were done in a mud job. The only plaster was above the tile. The fact that you got the tile off without destroying the plaster entirely is amazing. Sounds like it was put on by a homeowner after the initial installation.
Definitely remove the plaster and lath. If it's wood lath, take the plaster off first by hammering the walls from the bottom up. This will break the keys and it will fall to the floor. After all the plaster is all cleaned up, remove the wood lath.
These walls will not be plumb. The framing might not be even close to being on the same plane. You might have to shim the wall to get it close to plumb. Install the concrete board to just below the tile level if you're not going all the way to the ceiling. Use a mold free sheet good product for the rest of the way up. Tape all seams
Ron