You can leave the lathes on and overboard. I've come across this a lot, but you will have to cut off the parts that overlap or the boards will sit unevenly. I prefer to remove the lathes and then board myself. I would also remove the architrave and board/skim behind it then replace or renew as necessary.
It would work I suppose, but you'll end up with a pretty large gap for caulking if you just skim a single board. I'd prefer to remove architrave and then feather the board out with bonding just below level with the door casing as a single layer of 12.5mm board is not going to be as thick as the original plaster you've removed. You can do it your way, but it's just easier to get the trowel in with the architrave out of the way.
Its a ladder, lol.
Very suprised you went to the effort of removing all the plaster and left the lathes intact, I usually just get a wrecking bar in there and be done with it.
are you serious about skimm over the wood?