"Air-slaked lime is concidered an undesirable commodity; it certainly is an undesirable impurity, when mixed with quick or slaked lime. Yet air-slaked lime, when separated from unslaked particles, has been made into mortar and used as such, giving a strong and durable mass." - lime stone resources and the lime industry in Ohio, by Edward Orton, Samuel Peppel
in short - you can use it but it would have limitations which will affect your painting. you may be ok with it mabe not - depends in what you do, you will have to experiment, but you will never know what is the difference unles you will experiment with both - slaked and air-slaked.
The problem with airslaked or any dryform lime (like hydrolic type s lime from home depot) aside from possible high magnesium content (type - S) it is also continue to "air-slake" in the package slowly turning into a "bag of powdered stone" and unless you get it right off the shoot at the quarry and mix with water rightaway.
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