Transit is usually pretty quick in Beirut as you don't need to pass passports, there is a counter next to the passports for transit. Sometimes theres no one there and i'm not sure if they can check you in there or not. I transited once with MEA and there was a lady checking the boarding pass ( maybe to make sure you made it and transfer the luggage), after that the security is quick and you get directly in the duty free.

It's important to note that while you can check in online; Beirut airport doesn't accept printed BP so a passenger traveling without a suitcase still needs to report to check-in and get an actual BP

Passing the passport can be a hassle in the summer time as Beirut is at full capacity with all the seasonal flights added and passport control can take anything from 10 to 45minutes.