Embassy of Lebanon
2560 28th St NW
Washington, DC 20008
Traveling with your pet to Lebanon can be done as long as you have two documents. Your pet must have a valid health certificate, issued by a veterinarian in the country of origin. This certificate is to be approved and stamped by an appropriate government authority of that country (USDA if in the US). You will also need proof that your pet has been vaccinated against rabies.
It is unknown if there are any quarantine requirements. Contact the Embassy for more information.