As far as I am concerned the closest Mexican Consular service is the following one

Mexico Embassy
New Naccache, Sector 2, Street 53, Mansour Bldg, 1st floor
PO Box 11-3318
Postal Code:
70-1150
Antelias
Beirut
Lebanon
Phone:
+961-4-418870
+961-4-418871
+961-4-418872
Fax:
+961-4-418873
Email:
[email protected], [email protected]
Website URL:
www.embamex.org.lb, www.embassyofmexicoinlebanon.org

Contact them and then you know what to do...

Best regards