I understand where you are coming from. We can only look at published fares, but all markets have travel agents and consolidators and you should research both ends: what is available in Beirut as well as in London's ethnic travel bazaars.
Tell everyone upfront that you are looking at buying 35-50 roundtrip tickets per year and shopping for the best deal. That's quite a bit of bargaining power. I wouldn't hesitate even to call up airlines' local management and ask what they could do. No harm in asking.
Good luck. Let us know how it goes.