That's a very light definition of carbon neutral. All the equipment and energy (for humans and machines) to mine anything costs carbon to bring about.

It's an important point. There is nothing intrinsic about lime that requires carbon release beyond what is naturally released and consumed by the lime cycle itself, which is neutral.

Does the world's industry currently run on mostly hydrocarbons that do have a serious carbon footprint? Absolutely, yes. And it is something that needs to be changed. But that is a separate problem.