Here, quick has its original sense of living, and the popular term quicklime for this substance is a direct translation of the Latin calx viva, “living lime,” as taken through the French chaux vive.
To the chemist, quicklime is calcium oxide, and it was called “living” by virtue of its intensely vigorous reaction when brought into contact with water, seeming to be possessed of a living spirit.
Lime, in its older sense of “mortar,” or “glue,” is closely related to the German Leim, “glue,” and both have been traced to the Latin limus, “mud.”
Calx has come down to modern English as chalk, the great chalk deposits in England being the principal sources of lime to that country.