Hi

I don't think you have pigeons, but the lime could apply to both pigeons, and chickens, as well as housing for other animals. The lime kills all sort of insects. That must be the reason for using it on the coop floors. I already explained my way of treating the coop bedding in previous posts here, and you may have read it.
If I was to use lime, (in granular form) I would definitely use only
garden lime. I would avoid using Hydrated lime, in those places since it is caustic, and can cause burns.
I have in the past used the hydrated lime, and made a whitewash. Applied it to the interior walls of a garden shed that I had. Kept insects in control. (meaning, I did not see many insects, including spiders inside.)
Hydrated lime as a whitewash, when dried is no longer very caustic, and does not seem to cause burns at that point. Keeps insects away, as being undesirable for them to travel across.
WISHING YOU BEST,,,,,,,,,,,,,,,,,,,,,