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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-
all of which probably predates the lime mortar
Cement is relatively modern - lime has been around for thousands of years.
Roughly repointing would be part of the rendering / plastering work - if you're slapping a render on, you'd need to fill the holes in any case. If you're battening, then it may not be worth it, other than to tighten up any loose bits.
Condensation if probably not your concern if it's an outhouse. Being lime mortared, it suggests a solid wall, and lime is permeable, so damp can get through the wall. (Although being stretcher bonded suggests cavity wall - Unless its a single skin, of course.)
If it's lime, it will fizz in vinegar. If it's cement, it makes a ting noise.
NotThamesWater
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.