The instruction that came with my elector said if red mites treat the coop also. It was my understanding that the coop should be treated regardless of what type of mite/lice they might have.
Mites live deep in the cracks in the coop. Lice live on the chicken. Therefore, if your chickens have lice, it's not necessary to treat the coop. If you identify they have mites, the coop must be treated to get their eggs and juveniles.
Look at a bug under a magnifying glass. Count the legs. Lice have six legs. Mites have eight. Mites may leave a red stain when squashed. Lice do not generally suck blood so no red stain when you smash them.