I’d never had to patch holes in plaster and lathe before, and proceeded in the normal fashion, trying to slip strapping into the hole like you would with drywall. That was really difficult (at least in the small holes I was trying to patch.)
I got smarter on my second hole, and used the lathe itself as the strapping. All I had to do was cut the hole a bit bigger than my hole, like so:
then I was able to anchor my filler piece of drywall nicely using the lathe
my first coat in the closet side is a bit messy since that side it just plaster and lathe and very uneven
but on the outside side of this wall, where we have drywall on plaster on lathe, the patch will be nice and smooth:
I had some trouble using my new trick on one of my four holes, since the plaster and lathe in that section was thinner than my drywall. In that section, I tried trimming my filler drywall edgewise, which didn’t work too well, since it cracked once screwed in, but it was good enough to hold the mud in place, so it all worked out in the end.