Yes. Actually, I've heard of some "old-timers" who used to always have bunches of lavender hanging in their coops. It's the linalool from the lavender that is toxic to red mites. During the infestation, I would always spray my boots, my gloves, and the hood of my jacket before entering the coop. I just wanted to make sure I didn't bring them into the house. If you google it, you'll see that some people have had that happen, and not been able to get rid of them.
Also, whenever I clean the coop, I spray it - top to bottom - with "Thieves" from YL or "Four Robbers" (much cheaper and just as effective) from Birch Hill Happenings. Until the mite episode, in 7 years the only problem I have ever had was a banty with a cold. I attribute the health of my flock to the essential oils. I wouldn't be without them. They are my "medicine of choice" for my animals and my family! I have studied them extensively, actually used to private label my own until I discovered Birch Hill Happenings. You can go on-line for them.