Once the water is saturated with lime, it will stay that way more or less indefinitely -- I've known many people that use a large container for mixing all their kalk.. super saturate the water, let the precipitate/unabsorbed kalk settle at the bottom, and stir up about 10-15 mins before use... The excess kalk will keep your lime water fully saturated, and won't go bad.

As far as running kalk in an ATO system -- if you're not using a controller to meter how much is added at any given time, you could send your tank on a pH/alkalinity/calcium rollercoaster ride... be careful I would just keep dripping if it were me

-Justin