Ain't gonna be cheap!!
The mountains of Lebanon are a pretty as the Alps! Maybe that is why Lebanon used to be called the Switzerland of the ME. Enjoy your stay!
Don't worry, there is no "blockade" on Lebanon by Israel, or for that matter, by anyone else!!
But I doubt Zim will be able to get it to Lebanon. They do have an office in Haifa as was mentioned above since Zim is an Israeli shipping line. As you might already know if you are moving to that neighborhood, Haifa is not in Lebanon. It is in northern Israel!!
Another idea might be to ship to Cyprus and then arrange shipment from there to Lebanon. That is an option, but you will probably want "door-to-door" or "port-to-port" shipping. And expect to pay some "bakshish" on the other side.