According to Cornell's 'On-farm Composting Handbook' (Page 59) lime is added to overly green piles to slow down decomposition and hence undesirable odors. The provided link discusses alternate methods of pile odor control.
For instance, sprinkling a decaying animal with lime would slow down decomposition and reduce putrid odors. It throws the carcass pH off to retard bacterial growth.
Since it also liberates increased amounts of ammonia, it is generally not considered a useful component of a compost pile, but rather as an 'emergency' method of anaerobic odor control.

Here is a link that might be useful: Cornell composting handbook

I always thought the lime for those uses was HYDRATED lime, which is rather caustic.

I thought everyone was talking about dolomite lime, agricultural lime, or gypsum.

Maybe I was misunderstanding this from the beginning...

Sue

I've read/been warned not to use any alkaline substance including wood ashes on the compost as it converts nitrogen ammonia gas.

Numerous studies I have seen say that adding lime to compost changes the pH of that compost enough to cause the bacteria that digest the materials in that compost pile to stop working. Many years ago it was considered necesary to add lime, or wood ashes, to compost because it was thought that compost was acidic. Numerous studies since those days have found that finished compost was nearly neutral in pH.