Good luck to you. I also have a sick hen. She was one of four that came to us 10 days ago from a farm and is ~6 months old. She started out very droopy and sleepy, and has since pretty much stopped eating and sleeps all the time. We separated her into a crate and noticed that she was infested with mites. We dusted her with pyrethrum & DE ~5 days ago, but she hasn't improved. I've been feeding her boiled oatmeal thinned with water and yogurt via eyedropper. She barely opens her eyes. I noticed that she still had live mites on her (crawling on her eyelids!) so I dusted her again with Sevin today.
I guess my advice would be that if yours has lice or mites, skip the DE and pyrethrum and to straight to the strong stuff (Ivermec, Sevin). I'm also using DE for the bedding and dusting areas, but I wish I would have started with the stronger insecticide right away instead of hoping that the more "natural" option would be effective (it wasn't).
Again, good luck.