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.
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Large hole: If your slats are damaged, you may have to remove and replace parts of them. Check for damage to the studs behind the slats as well, if they're broken you may have to make a much bigger hole to fix a stud. Once replaced, re-plaster all affected areas of the wall.
For a medium hole, with only a few bits of slat broken.. there are plugs you can get comercially... or you can make one out of wire mesh. Either way, you will need something for the plaster to stick to.
For a small hole (two fingers wide or less), plaster will do on its own.
If the hole is not too big you should be able to repair it yourself. Hopefully the "lath" or wood slats are still intact or you may need to replace or add new lath by screwing in some new strips of wood.
Real plastering is a lost art. Cured plaster does not sand well because it is so hard. It is finished and burnished in the time it takes to set up firm. If you have a textured plaster wall, all the more harder to match without knowing the proper plaster technique to get it looking right.
For a flat wall. It is easier to use spackling paste or compound for small holes not larger than a coin. Use drywall joint compound or patch applied in layers to build up bigger holes. You may also embed some drywall tape or fabric mesh tape to reinforce the repair. Use a spray bottle to wet the drywall knife to smooth out the final layer as best as possible to reduce the need for sanding. The fine dust will get everywhere. Prime and paint afterwards. You can look up youtube videos on wall repair, plaster, drywall to see it actually being done. Good luck.
Remove all the loose plaster, wet the slats and surrounding plaster and replaster it. dont try to do it all in one go build up a few layers if its quite deep.
If you take your time then you should get a good finish. you can always sand it afterwards to get a reasonable finish.