I am not a great believer in patching/filling out missing areas of plaster, with pieces of plasterboard,,, in an otherwise sound, lath and plaster wall/s etc,, i'd fill it with plaster,, but that's just my preference. If you do want to use p/board,, make sure the depth of original plaster is thicker than the piece of plasterboard you intend to use for patching,,, pretty obvious, but you do get some who fill in a patch with p/board, and it ends up proud of the surrounding plaster.
. Trim carefully around the edges of the existing plaster, just to remove any more loose bits, and also to give it a more regular shape for fitting the p/board into. I "wouldn't" cut away the old laths if they're ok, they will make a good sound backing for the p/board to be screwed onto. Use plenty of "screws",,,rustproof,, 35mm or so,, and screw the plasterboard straight onto/into the wooden lath. I would leave a small gap all around the patch between the old plaster and new p/b,, say 20 / 25 mm,, just so you can wet down and pva all around the edge of the patch,,, even wet and pva the dry edges of the plasterboard. Mix up some bonding coat plaster, and apply it all around the edge of the patch while the pva is still tacky, (by doing this, you're now filling up that 20/25mm gap). Put some fibre tape over the edges/joint of the p/b/wet bonding,,, to tie it all in together,, then cover the whole area with bonding coat, ruling it off with a small straight edge as you go. Build it up gradually between coats, scratching/letting each one steady up as you go, keeping it a mil or so below flush to allow for a couple of thin coats of multi. Keep all around the edges clean, using a wet brush,, looks tidier. Hope you understood what i've said.
Roughcaster.