My typing skills are just as bad as my failing memory as while I was adding my post I did not see the one from Ms Sunshine. Great that entry visas are free as we enjoyed our quick visit and would like to return to Beirut for a longer trip.
Dh and I went to Beirut for 2 days last September and obtained visa at Beirut Airport. From memory I think we went to desk to left of passport control for visa first and I think it is free for visits of up to 48 hours but for more than 48 hours costs something like 25.00 LP so you will need local currency.
Check this link http://www.general-security.gov.lb/English
Have a good trip