A product called Plasterweld will make a difference, and will help tie down the neighboring plaster which is probably a little loose too. It acts like glue. don't let it drip down the wall. A water activated patching compound, squished through the lath and recessed a bit (score it a little as it sets) will make a good base for joint compound. You can sand dried compound with a damp sponge to avoid dust. Prime and paint. When I paint a patch, I brush it on and then roll a dry paint roller over the paint to match the texture of the surrounding wall. Works great.