The 2017/2018 QS Arab Region University Rankings are out and the American University of Beirut has topped the list ahead of King Fahd University of Petroleum & Minerals and King Saud University. AUB ranked #1 among 1,000 universities in the Arab World for the first time in its history.
The methodology for the QS University Rankings for the Arab Region retains key indicators of the global university rankings while considering a set of performance metrics carefully tailored for the area, adapting to reflect regional priorities and challenges. Nine indicators were used in this QS regional ranking method, with the following weights of the total score: academic reputation (30%), employer reputation (20%), faculty-student ratio (20%), web impact (10%), papers per faculty (5%), citations per paper (5%), percent of faculty with PhD (5%), percent of international faculty (2.5%), and percent of international students (2.5%).

As far as other Lebanese universities are concerned:
Saint Joseph University ranked 12th
Lebanese American University ranked 16th
Lebanese University ranked 25th
University of Balamand ranked 30th
Notre Dame University (NDU) ranked 39th
USEK ranked 40th

You can read more [here].