Sirolimus and Auranofin in Treating Patients With Advanced or Recurrent Non-Small Cell Lung Cancer or Small Cell Lung Cancer

Inclusion Criteria: * Histologic or cytologic confirmation of lung cancer (squamous, ras-mutated adenocarcinoma or small cell lung cancer) * Patients must have received at least one course of chemotherapy consisting of a platinum doublet and must have no acceptable standard treatment options * Prior radiation therapy is permitted as long as: * Recovered from the toxic effects of radiation treatment before study entry, except for alopecia * Absolute neutrophil count (ANC) \>= 1500 uL * Platelets (PLT) \>= 100,000 uL * Hemoglobin (Hgb) \>= 9 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) or direct bilirubin =\< ULN * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamic pyruvic transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 3 x ULN or SGOT (AST) and SGPT (ALT) =\< 5 x ULN is acceptable if liver has tumor involvement * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1, 2 * Negative serum pregnancy test done =\< 7 days prior to registration, for women of childbearing potential only * Ability to provide informed consent * Life expectancy \>= 12 weeks * Willing to return to Mayo Clinic enrolling institution for follow-up * Willing to provide tissue samples for correlative research purposes Exclusion Criteria: * Any of the following: * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception * Symptomatic, untr…