I understand that lifetime license holders are subject to paying nonresident tag fees once they move out of Idaho, but are they treated as nonresidents in controlled hunts?

Lifetime license holders who move out of state continue to get their lifetime license each year at no charge.  They have to purchase nonresident tags and permits, however.  Usually nonresidents are only able to draw up to 10 percent of the permits in any controlled hunt; lifetime license holders are exempt from that limitation and are considered for a controlled hunt with residents.