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the mortar appears to be basically dust (softer than the plaster)
If it's lime-based, it should be pretty much the same stuff. If it's harder, it's possible that someone has added gypsum (which would explain the cracking) or even cement (again, which would explain the cracking).
If you dryline it, you should consider battening it too, or risk damp boards. Maybe even chuck in an airbrick.
I'd consider repointing (roughly) with NHL 3.5, rendering with pretty much the same thing (maybe with a pozzolan added) straight on the brickwork. It won't be polished like gypsum (I'm guessing as it's an outhouse, it won;t matter), but if you want a smoother finish, you could skim a chalk render on top and finish with a lime wash.
NotThamesWater-
I would batten yes. It's cold and drafty, so should suffer from condensation to badly. Would the pointing add any strength?
It's quite possibly not lime render actually, or at least there's bits of cement, all of which probably predates the lime mortar. There's Tyrolean on the outside anyway which pretty much makes the whole back of the house a bit screwed to a greater or lesser degree.
I'll sell this place in a couple of years probably, so not fussed about making it perfect, just need a clean-ish place to store tools out of sight.
Polygon
Started to clear the old plaster from inside my outhouse, bit worried as the mortar appears to be basically dust (softer than the plaster) and there are some big cracks in the plaster near the top indicating movement. Wondering if it would be wiser to basically dry line it with something like OSB?