Lice do not want to live in a wig the way they live on a human scalp. They need blood meals from the scalp. But a wig can still be a temporary carrier if it touches infested hair.
When a wig becomes a risk
Sharing wigs, trying on wigs without a cap, storing wigs with infested hats or bedding, or wearing a wig over untreated lice can transfer insects or nits.
What to do
Treat the scalp first using medical guidance. Then isolate the wig, wash it according to fiber type, and avoid high heat unless the wig label allows it.
Bottom line
A wig is not the ideal home for lice, but it can carry lice briefly. Do not share wigs during an outbreak, and clean anything that touched infested hair.