Temsirolimus and Pemetrexed for Recurrent or Refractory Non-Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed diagnosis of NSCLC. * Patients must have non-squamous histology. * Patients must have measurable disease (by RECIST criteria), defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥20 mm with conventional techniques or as ≥10 mm with spiral CT scan. * Patients may have failed at least one prior platinum-based therapy for NSCLC or be candidates for first-line therapy for advanced disease deemed ineligible to receive platinum-based chemotherapy in the opinion of the treating physician (e.g., Eastern Cooperative Oncology Group (ECOG) performance status of 2, age ≥ 70, chronic medical condition). * Patients must be at least 4 weeks out from chemotherapy, biological therapy, major surgery, or any investigative therapy and must have recovered from any toxicities. Patients must be at least 2 weeks out from prior radiation therapy and must have recovered from any associated toxicities (with the exception of alopecia). * Patients must be at least 3 weeks out from immunosuppressive therapy (except corticosteroids used as antiemetics). * Age ≥18 years. Because no dosing or adverse event data are currently available on the use of pemetrexed in combination with temsirolimus in patients \<18 years of age, children are excluded from this study. * ECOG performance status 0-2. * Patients must have normal organ and marrow function as defined below: * hemoglobin ≥9.0 g/dL * absolute neutrophil count ≥1,500/mcL * platelets ≥100,000/mcL * total bilirubin ≤1.5 mg/dL * aspartate aminotransferase (AST)(SGOT)/ alanine aminotransferase (ALT) (SGPT) ≤2.5 X institutional upper limit of normal OR ≤5 X institutional upper limit of normal if enzyme abnormalities are due to liver metastases * creatinine \< 2.0 mg/dL AND/OR * creatinine clearance ≥60 mL/min/1.73 m2 for patients with creatinine levels above institutional normal * serum cholesterol \< 350 mg/dL * triglycerides \< 300 mg/dL * The effects of pemetrexed and temsirolimus on the developing human fetus at the recommended therapeutic dose are unknown. For this reason and because antifolate antineoplastic agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. * Ability of the patient (or legally authorized representative if applicable) to understand and the willingness to sign a written informed consent document. * Both men and women and members of all races and ethnic groups are eligible for this trial. Exclusion Criteria: * Patients who have had previous treatment with pemetrexed. * Patients may not be receiving any other investigational agents. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, clinically significant hepatic or renal disease or neuropathy greater than grade 2. * Symptomatic brain metastases * Presence of a third-space fluid (pleural effusion, ascites etc.) that is uncontrolled by drainage. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to temsirolimus, its metabolites (including sirolimus), its components, and/or polysorbate 80, or to other agents used in the study. * Known hypersensitivity to macrolide antibiotics. * Patients with psychiatric illness/social situations that would limit compliance with study requirements and with premedications of dexamethasone, folic acid and vitamin B12. * Patients with inability to discontinue all non-steroidal anti-inflammatory drugs (NSAIDS). * Patients taking anticonvulsant medications (Carbamezapine, phenytoin, fosphenytoin, phenobarbital). * Patients taking anti-arrhythmic medications (amiodarone, diltiazem and quinidine). * Patients may not be taking medications known as inhibitors of CYP3A4 (carbamezapine, phenytoin, phenobarbital, rifampin, St. John's wort). Use of inducers of CYP3A4 is discouraged but not specifically prohibited. Dexamethasone as a chronic medication is discouraged. * Pregnant women are excluded from this study because pemetrexed is an antifolate antineoplastic drug with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with pemetrexed, breastfeeding should be discontinued if the mother is treated with pemetrexed. These potential risks may also apply to other agents used in this study. * Patients with known concomitant genetic or acquired immunosuppressive diseases are excluded. HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with pemetrexed and temsirolimus. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated.