Ive lived and ridden a bike in Lebanon for several years. Left the country back in 2003 and from what i understand the biking culture has evolved.
When i was there, the bike culture was very different form Europe. Loads of GSXR-750's thats been converted to street fighters and many Japan/Oceania bike models thats been imported by shops, such as the Honda AX-1, XR250 Baja, etc. Expect many stunters too.
People used to ride like crazy down there, helmet- and plateless, weaving in and out of traffic and pulling wheelies at every occasion.
The goverment did a major crackdown, as many bikes were used for criminal activities, and theres a bit more order now, but nowhere near EU-standards.
My friends tell me, that you see quite alot of new bikes now, especially in the more affluent areas. People who invest that much in a bike, usually abide by all rules ie. license, plates, helmet, etc.
If you do decide to rent a bike, then drive defensively and stop at all checkpoints. Lebanon is a powder-keg right now, so dont give the security forces the impression that you're considering something sketchy. Lane splitting is perfectly legal.
Beware, that sometimes motorcycle curfews are in place, especially in the dark hours. Stay out of the Hezbollah-controlled suburbs, as they might mistake you for a foreign spy. Theyve got their own security patrols in that area.
Tripoli and the south near the Israeli border aint a good place to be driving around considering the current security status. The north-east near the Syrian border is a site of confrontations between IS and lebanese forces/Hezbollah too.
That being said, there are MANY beautiful places to visit. The whole coast line from Sidon to Byblos/Jounieh, the mountains east of Beirut, etc. are all worth a visit. Checkout
http://www.destinationlebanon.gov.lb/
As long as you have a modicum of situational awareness and have read up on the current security status, then you'll have a blast!