BEY would be brave considering the lack of ties between the two countries, the fact that Lebanese tourism has never recovered from the Civil War and that you are competing for westbound transfer passengers with BA, Air France, Alitalia, Lufthansa and Turkish.
If looking Middle East, Amman would seem to make more sense, as a country that has been largely more stable and because Royal Jordanian are in OneWorld, so their eastbound connections could be used and their network could feed on to EI transatlantic. Not that I think Amman is a remote possibility.