I usually go karting during the summer as most tracks are outdoor and closed in winter times. Karting in Lebanon is not that popular and there are barely few decent tracks, mainly the RKZ (Racing Kart Zouk) and the Race of Champions track in Mansourieh (not sure if its still open though).
The track in Zouk is right next to the Dream Park on your way up to Jeita. It has two different types of karts that you can use, the 6hp cars for beginners and the 9hp cars for experienced drivers. You become experienced after you drive more than 10 times and get a card that allows you to drive the 9hp. I’ve been driving the 9hp for years now and it is a huge difference from the regular cars in handling and in speed.
Price wise, you pay 15,000 LL or 10$ for 15 minutes during week days and 20,000 LL or around 13$ on Saturdays and Sundays.