It was a matter of common practice, up until the collective worldwide derailing of sanity going on just now, that reuse was the norm. Brick, wood and I have heard, but it may be a myth, even lime mortar. But you could include window panes, roof tiles - christ, who knows how far this cycle of re-use was or could be perpetuated.

I have spent many hours for days knocking old lime mortar off of brick and reusing the bricks. There are noticeable impurities imbedded in the mortar, mostly bits - up to 5 mm and sometimes as big as 1 cm - of shells. These impurities, the result of the less than clinical production precesses, play no small part in the overall character of the mortar. Because modern production is largely a clinically controlled process, where imperfections are frowned on, these defects are done away with and result qualitatively in a different product. This old lime mortar is truly wonderful stuff I notice as I struggle to remove it, and I am left to live with the knowledge that the best that I can do will never match up in reality.

But back to lime plaster and lime plaster applied to interior walls, as the subject was. Except to say those Roman weenies never could occupy Friesland. Ha. Pleased to say that I just hauled some of my lime, in a bucket with the lid on and topped off with water, up from the well after a few years, and it remains a nice, smooth and sticky paste. Only 30 or so more years to go now. It's true that the sand used is particular in that not any old sand will do. Sharp edges give the lime, (binder) a chance fuse with the sand,(aggregate). Binder, aggregate, strength! Water, catalyzer plus makes it easier to use. Watch out, not too much.
I like the idea of storing it in the ground and digging it up later to use. Only thing is that eventually the lime would leach and seep into the ground and leave only sand behind. Better store your clay in the ground and give the lime an impermeable bottom to stand on while it brews.

Now I wonder about finishing off the plastered surface. I can think of no lime based surfaces left without some kind of finish treatment. In fact I think any such surface would be technically incomplete.