Amy, I'd go ahead and strip that old stuff right on down, maybe even to bare studs; this would allow you to insulate that wall, as it probably isn't insulated now.
The wire lathe & cement would be a rough, messy surface to try and go back to. Once you've torn off all the layers you want to, then you can measure to see just how much thickness you need to replace to be over the lip of the tub; replace that thickness with a cement backer board, not drywall. Durock & Hardiebacker are 2 brands of this, and the HardieBacker is available in different thicknesses, and would probably be the easiest for you to work with; very nice product.
Good luck Amy!