Advanced lung cancer remains an incurable disease although new agents and new treatment strategies have resulted in improved survival outcomes for patients. Most recently there has been interest in augmenting tumor response to chemotherapy by the addition of drugs which inhibit tumor cell growth and proliferation. Everolimus is a new cancer drug which works as an inhibitor of mammalian target of rapamycin (or mTOR), mTOR is a protein that is part of a signaling pathway which can cause cancer cells to divide. Everolimus when used alone as a single agent has produced some response as well as prolonged stable disease in both chemo-naïve and pre-treated non-small cell lung cancer. The goal of this study is to evaluate the safety of everolimus with combined other cancer drugs called pemetrexed, carboplatin, and bevacizumab. Pemetrexed and carboplatin are both chemotherapy drugs and bevacizumab inhibits the growth of new blood vessels.