Lime is no issue for the garden it's the chickens it may not be good for. The laws say it's for odor and fly control. I started looking at that when I read that and remembering we used to use it when our dirt floor old barn was stinky and the flies were crazy--back when I lived in the country. It is an extension service link:
http://articles.extension.org/pages/66918/use-of-lime-in-poultry-houses.
I'm betting if there is no pest issue or odor problem if it's checked by codes it wouldn't be an issue. Since I live in a neighborhood with just normal yards I was thinking it may be a good idea but will hunt other methods if the flies get bad.
Good that your neighbor is OK with chickens.
Thanks, I was under the impression that doing the deep bed in the coop would make it nearly odorless, and manure would dry out generally if they are just running around the yard or in runs...