I would take off the lathe and plaster and hang new drywall. You can install "buttons" to put the old plaster back up firmly, at least for a while.
One thing that I would also do is check the floors and get the house level if there is a problem. If you later move the house around with plaster, it will certainly crack again. It might also show some movement with drywall, but it will not be as bad. Leveling the floors before you start this is probably something for the pros or someone experienced. You probably will not have to tear the whole house apart, like Tommy does on a certain TV show, but you probably will get to hate plumbers who cut out the basement joists years ago.