No, the war in Libya was a militia operation to overthrow the government. The only thing NATO did was enforce the UN resolution to close their naval and airspace, and run sorties against Gaddafi.
You know Qatar and Tunisia also played roles in the civil war? Last I checked, they were not NATO members. The Arab League and African Union also played parts in the conflict, with the former supporting NATO involvement to enforce the UN resolution.
Implying NATO started things or led the charge is ahistorical.