Traditionally Turkey and Saudi Arabia are largest export markets for US corn oil, but due to biotechnology constraints in Turkey, Tunisia quickly stepped in to the number one slot in 2011.
A large portion of the US corn oil exports to Tunisia are refined in country and then sold into Libya; this is also common for refined corn oil brought into Tunisia to then be trucked into Libya.
Sunflower oil (Ukrainian) is usually the cheapest vegetable oil option on the grocery shelves in Tunisia, but Libya has grown to favour corn oil over other vegetable oils over the years, giving US corn oil a qualitative advantage in this market.
According to the US Grains Council, roughly 70% of the total corn oil exported to Tunisia, eventually ends up in Libya.
There are also some direct sales to Libya and Egypt has been a growing market for US corn oil the last few years.
Note that the accompanying chart combines both crude corn oil and refined corn oil exports.