Interesting! I've never used lime myself.
What I do use to keep things dry is a mixture of Stall-Dry and peat moss thrown right onto straw bedding. The chickens do all the hard work of mixing everything up, and there is no odor at all.
Makes wonderful compost too.
Oh, and really good ventilation also helps with dryness. In my experience chickens seem to do the best with lots of fresh air. -40C is common for my area in winter (quite literally a deep freezer, haha) and I keep wide open vents and cracked windows year round. Just have to be careful there are no drafts in the roosting area and all is well.