Lice is generally host specific, so mice are not bringing it in. However, mice will contaminate and consume a lot of feed. It is a good idea to keep the rodent population in check. Lice also feed on blood - manure has no influence on this. And lice only live on a host, dying very quickly off the host so you are not bringing it in on sand or bedding.
I have never had lice, (whispering) I do let mine out to free range, and we have a very dry and sandy climate. Down the road, my niece has had lice, but strictly keeps hers confined, and maybe slightly too many for the set up. I do have to admit, that while she has had lice, she has never lost anything to a predator.
I use old hay or waste hay. We ranch, that is what I have readily available, I pile it deeply in the coop, with a broom out 2-3 times per year. I often top it with scratch, and the girls turn it keeping everything dry. DRY is important. When I clean out the coop, I just dump that in the run.
My run has bare spots, and covered with hay spots. It is 600 square feet, so a lot of space. In the spring I use it for mulch in the garden. The theory being the weed seeds are gone...not that I have any proof of that, or rather I have proof they didn't get all the weed seeds but hey, that's they theory.
I just have clean water - nothing added. I just have old hay, no DE or tidy stall. But we are arid, and I think climate has a huge influence. I have never scooped chicken poop.
Mrs K