OP: I used to live in a house with plaster just like this. First step: pull out all the loose plaster. If it ain’t attached, it won’t stay attached. Second: use a product called USG structo-lite base coat plaster and apply it to the bare lath, all the way up to the old plaster. It’s lightweight and spreads like peanut butter but dries hard as concrete without shrinking and cracking. Be sure to apply it just slightly shallow to the height of the original plaster, because once it dries it’s hard to lower. Third: Skim the top of the structo-lite with drywall mud and sand it smooth. Bingo!