So, who is ultimately authorised to certify the ACs airworthyness with INOP NAV lights and do oncoming traffic need to be informed as such?
You have to have them to comply with the rules of the air for night flying. To answer your question directly, you would need the dipensation of both the authority whose airspace you are operating within plus that of the authority of registration if different. Probably no chance of that anyway if they can be fixed at the departure airport and even less chance of being able to take passengers. Bottom line is it would be easiest to simply get them fixed before flight.