The “ carnet de passage en Douane released by LAC (Libyan Automobile club) is released only for Libyan citizen and foreign peoples with current residence in SPLAJ ( LIBYA) going abroad for temporary time ( max one year) . It is a not a local carnet but an International one and if the traveller/bearer is not the legal owner of the car this must be specified with a note specially preview in it. The same procedure is required for carnets released in other countries of the world and for temporary stay in Libya, as it is the same international Carnet de passage en Douane. (see the related Convention . it is written in French).
The carnet , at the moment is not necessary in Libya, but in the case You are enquiring , a declaration duly signed by the owner and registered to by a local lawyer is required, specially in case of accident where the insurance could not pay nothing nor to the driver nor to the owner , as occurred to a car of an Italian traveller lately involved in a local deadly crash . Take not also that there is a difference with a car imported by a private /single people and from and organization /or ( the termination may change ) and more generally speaking what happens as experience to one doesn’t means that has to happen necessarily to the other, and this mainly when the information lakes of official nature .