Additional Study Information: The purpose of this study is to evaluate the combination of study drug MEDI4736 and tremelimumab in treating advanced non-small cell lung cancer that is resistant to or returned after receiving standard therapies, for which there is no available standard therapies, or for individuals who have declined standard therapies. MEDI4736 and tremelimumab are fully human monoclonal antibodies that are manufactured similar to antibodies that are made by the human body. Antibodies are natural proteins made by our immune system that bind other proteins and molecules to fight infection and its ill effects. The idea behind developing these types of experimental drugs is that stimulating the immune system could be a different way of killing cancer cells, and by administering both antibodies, two important pathways can be targeted that may help your immune system eliminate tumors. The main purpose of this study is to determine the best doses of MEDI4736 and tremelimumab and determine how safe and tolerable MEDI4736 and tremelimumab are when given together in subjects with advanced non-small cell lung cancer.