— Aaron and Becky, Little Falls, MN
A: Tom Silva replies: Sure, you can cover the old plaster with drywall, as long as you use screws long enough to penetrate an inch into the framing. But you need to be aware that adding an extra 1/2 inch of wall thickness will swallow up much of the heft of the trim, or casings, around the doors and windows. Plus, you'll have to remove all the baseboard trim and any crown molding and then reinstall it on the new drywall.
Here's another alternative: Reattach the cracked plaster to its lath with plaster washers or adhesives and cover everything with wide rolls of fiberglass window screening. Bed all the screening in a thin coat of joint compound, wait a day for it to dry, then skim over it again. You'll probably have to do a third coat to get it smooth. Don't get too aggressive with the final sanding; you can easily expose the screening.
But if you think there are too many cracks to make that approach worthwhile, then your other choice is to leave the trim and lath in place, strip off the old plaster, and replace it with sheets of 3/8-inch drywall screwed into the studs, not the lath. Around doors and windows, where the trim is covering the studs, glue the edge of the drywall to the lath where it slips behind the trim. If you want to insulate and install a vapor barrier on exterior walls, or upgrade the wiring and plumbing, then the lath will also need to come off. In that case, cover the studs with 1/2-inch drywall.