Sirolimus and Pemetrexed to Treat Non-Small Cell Lung Cancer

Background: The drug pemetrexed is used to treat non-small cell lung cancer (NSCLC) that does not respond to standard therapy or that has recurred after standard therapy; however, only 9 in 100 patients respond to pemetrexed. Sirolimus is a drug that blocks a protein in cells called mammalian target of rapamycin (mTOR). In cancer cells, mTOR is active when it should not be, allowing the cells to grow uncontrollably. This protein is unusually active in many cases of NSCLC. By blocking the activity of mTOR, sirolimus may make the cancer cells more responsive to treatment with pemetrexed. Objectives: To determine if sirolimus in combination with pemetrexed is safe and well tolerated in patients with NSCLC. To determine the highest safe dose of pemetrexed combined with sirolimus. To look at the ability of sirolimus and pemetrexed to fight NSCLC. To learn how the body eliminates sirolimus and pemetrexed. Eligibility: Patients 18 years of age and older with NSCLC whose disease does not respond to standard therapy or has recurred after treatment with standard therapy. Design: Biopsy before treatment starts, if the tumor is easy to reach by bronchoscopy or can be done by needle biopsy. This procedure is optional. Drug treatment, as follows: * Day 1: Intravenous (through a vein) infusions of pemetrexed. Small groups (3 to 6) of patients are given pemetrexed at a certain dose level. If the first group experiences no significant side effects, the next group receives a higher dose. This continues in succeeding groups for up to five dose levels until the maximum tolerated study dose (highest dose that patients can be given safely) is determined. * To lessen the side effects of pemetrexed, patients also receive a Vitamin B12 injection every 21 days, folic acid tablets daily, and dexamethasone tablets twice a day the day before, the day of, and the day after pemetrexed infusions. * Days 1-21: Sirolimus tablets by mouth. Evaluations during the treatment period: * His