It is possible that because you birds are LIVING with the goats, that the lice are feeding on both animals. Mites and lice can't solely live on poultry if they were meant for mammals, but that definitely still bite them. It is not uncommon for people to get bitten by poultry mites ( I would know ) But they cannot sourly live off of people. I think that a light treatment of wood ash for the chickens, AFTER they get moved back to their old coop would clear up any lice that they carried back.I am definitely no expert and have done no research on this topic, but I am going to throw in my very recent observation regarding chickens and "mammal" lice.
My chickens have never had a lice problem until very recently. For various reasons we are having to undergo a coop rebuild and - in the meantime - our flock is currently cohabitation with the goats in the goat pen. Within the last week or so of them cohabiting, I've noticed a couple of the girls getting really puffed up. No sickness, no lethargy, just feathers so fluffed they looked like they had been electrocuted. Now every single one is scratching and constantly preening.
IMO, there is no doubt about it. They caught lice from the goats. That is the only thing that makes sense to me. I wouldn't have thought it possible until I sat back and watched it happen. Now I have to figure out how to de-lice 45 birds - and 4 goats...