First, here are still some cedar forests in Lebanon. Mostly in the central mountain areas. The largest protected forested area is the Shouf Cedar Nature Area southeast of Beruit. It contains the forests of Barouk, Maaser el Shouf and Ain Zhalta-Bmohras. In total according to the FAO 2010 Forest Resources Assessment, currently 13% of Lebanon is forest, while another 10% is "other wooded land." Lebanon has made international commitments to encourage regrowth of the forests and have been averaging a 0.83% reforestation growth rate over the past decade or so. Cedar is a relatively rare tree in the forests as they are now dominated by white oak. None the less there are still a fair number of cedar stands. All this was taken from the Lebanese Ministry of Environment.

So with the caveat that 1/3rd of the historic forests are still there, where did they go? Mostly they have been done in by two things: changed land use patterns and climate change. As early as the Romans, they were seen as an endangered resource. Emperor Hadrian set aside the forested areas as an imperial reserve. But logging has continued to this day. As areas have been cleared over the centuries they've been opened to agriculture and grazing, which has prevented the forests from returning. The old forestland is now farm land.

Plus as you've noted the climate in the area has gone hotter and dryer over the few millennia. In Cedrus libani (A. Rich) distribution in Lebanon: Past, present and future by Lara Hajar, Louis François, Carla Khater, Ihab Jomaa, Michel Déquée, Rachid Cheddadi, the authors note that the cedars in particular couldn't return to their early historic range. Rainfall, temperature, and humidity have changed. Cedars used to grow in the Bekaa and Ghab valley floors. These are now inhospitable to forest growth. As temperatures have warmed from the Bølling/Allerød climate prevalent in the mid-holocene the forests have slowly migrated up from the valleys to the more mountainous areas. So even without local human action (logging/farming) Lebanon wouldn't have the 75% forest cover it used to have.