The quicklime method shouldn't be particularly fast, at least that's what my chemical intuition says (CaOH2 is barely soluble in water). What a bad name!
In the most general context it means "with the characteristics of the living" (as seen through a middle ages lens).
In the context of "quicklime" the quick refers to the heat of the reaction when making lime for slaking on walls, etc.
"Quick" historicaly has been applied to plants and animals (alive), rivers and streams (moving), coals, fires, quicklime (burning, heat producing, glowing), to speeches and pamphlets (Lively, full of vigour or sharp argument), to tastes, to smells, and more.
The full blown Oxford English Dictionary entry for quick is a lengthy one, multiple cases and variations over a page and more.
