Bill wrote
When I had a similar situation my plasterer, I know I should have DIY'd
it, found the supporting frame work through the plaster and lath and
screwed plaster board on and skimmed it. I lost maybe 1/2" of the room
but it was much cleaner than removing the old plaster, but not as much
fun, and probably added a bit more thermal insulation too.

Yes, good idea - I've done the same on my upstairs ceilings. I just assumed
from his message that the OP had already removed the old plaster - dunno why I
did that now! )

Peter