Patching or replacing sections of old plaster is a bit of work, but less mess than removing plaster and lath unnecessarily.
To patch a small (couple-inch) section of plaster, gently remove loose plaster. (It comes off in unpredictable chunks, so score the outline with a utility knife first.)
Next, apply a hard, fast-setting patching compound along the edges of the old plaster to hold it to the lath. Keep the compound below the surface of the wall; it’s impossible to sand. Apply successive layers of compound until you’re almost — but not quite — flush with the surface of the wall. Then finish with drywall compound.
For larger sections, use drywall. Remove the plaster back to the middle of the studs either side of the hole. Cut the lath along the middle of the stud, and remove it from the opening. Install a piece of drywall in the hole, shimming as necessary, to bring it within 1/8″ of the wall surface. Use patching compound to seal the seam and hold the plaster in place all round the drywall. Then apply a skim coat of drywall compound over the surface of the drywall sheet and the seam.
If you’re dealing with large sections of a wall, try and make your joint in a corner. But if you’re dealing with a large wall, and would rather not remove that much plaster, make a flat plaster to drywall joint. Use the same technique you’d use for larger patches (above), but in this case, shim your sheet of drywall so it’s level with the wall surface, and screw the bevelled edge along the seam with the plaster. Your plaster patching compound will seal the seam, or bevel the edge of the plaster and tape and mud as you would with ordinary drywall.