Use AMERICAN FLIGHT SUPPORT to arrange your permit. Two days notice is required for overflights and tech stops.
If you are operating commercially or with passengers (even private) you’ll need to give seven days notice of your flight.
No flight may route to or from Israel. Remember, Lebanon is now part of Eurocontrol, so you only need to file your flight plans to AFTN: EUCHZMFP and EUCBZMFP.