Expedited LNG for American Allies Act of 2013 - Amends the Natural Gas Act to deem consistent with the public interest an expedited application and approval process without modification or delay for the exportation of natural gas to a foreign country that is: (1) a nation with which there is in effect a free trade agreement requiring national treatment for trade in natural gas (as under existing law); (2) a member country of the North Atlantic Treaty Organization (NATO); (3) Japan, as long as the Treaty of Mutual Cooperation and Security between the United States and Japan remains in effect; and (4) any other foreign country if the Secretary of State determines that such exportation promotes U.S. national security interests.