In lath and plaster construction, the baseboards and door trims were put up before the lath and plaster. Whatever you do for wall finish material needs to result in the same net thickness as the lath and plaster was so that it will fall at the same place on the trim and look right.
Tearing off the plaster only will give you a nice flat surface on top of the lath to hang 3/8". This is a very typical route. If you tear off the lath as well, you might run into problems. The old studs were often locally milled from native timbers, and are often not uniform. If you drywall with some 5/8" right over these local, native studs, you can often end up with very defined "waves" in the finished wall. Leaving the lath on helps with that matter, as the laths were sometimes shimmed here and there to even out the wall and different lath thicknesses were chosen for certain sections of the wall to help. Plus, if you leave the lath on, you can tear off a strip midway and at the top and blow the cavities with blown insulation (savings over fiberglass batts), and the lath will hold the blown insulation in the cavity.
In lath and plaster construction, the baseboards and door trims were put up before the lath and plaster.
Thats not always true. I just got done tearing out baseboards in my 1930 Colonial House-lath and plaster extended 3 inches down the wall from the top of the baseboards in interior walls-and the exterior walls had full lath and plaster once the baseboards were removed.