Here are some of the airlines (from memory) that fly to Beirut at the moment:
From West Europe:
British Airways, Air France, Alitalia, KLM, Lufthansa, Austrian, LTU (soon), Olympic, Turkish, Cyprus Airways
East Europe and CIS:
Malev, CSA, JAT, TAROM, Aeroflot, Armenian, UM
Tunis Air, Air Algerie, Egypt Air, Ethiopian
Syrian Air, Kuwait Airways, Royal Jordanian, Emirates, Gulf Air, Saudia, Oman Air, Qatar Airways
MAS and I'm not sure if Air Lanka is still flying
There might be others but as I said these are from memory at this moment.
BEY may become a major hub. It's all related to the political situation in the region.
All the best.