Sirolimus and Gold Sodium Thiomalate in Treating Patients With Advanced Squamous Non-Small Cell Lung Cancer

Inclusion Criteria: * Cohort I (Dose Escalation) only: must have histologic proof of an advanced, solid tumor that is now unresectable * Cohort II (MTD) only * Patients must have platinum-refractory NSCLC (platinum-refractory defined as either disease progression either during or within 6 months of completion of first-line platinum-based chemotherapy) * Must have measurable disease * Must have received at least one prior approved chemotherapeutic regimen unless there is no known, approved therapeutic regimen for their malignancy * Must have evidence of disease progression within the preceding 6 months - Absolute neutrophil count (ANC) \>= 1500/uL * Platelets (PLT) \>= 100,000/uL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * (Serum glutamic oxaloacetic transaminase \[SGOT\]) aspartate aminotransferase (AST) / (serum glutamic pyruvic transaminase \[SGPT\]) alanine transaminase (ALT) =\< 3 x ULN or (SGOT) AST / (SGPT) ALT =\< 5 x ULN if liver involvement * Creatinine =\< 1.5 x ULN * Fasting blood glucose =\< 126 mg/dL * Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) 0, 1 or 2 * Ability to provide informed consent * Willingness to return to Mayo Clinic in Florida for follow-up * Life expectancy \>= 84 days (3 months) * Willing to provide blood and tissue samples for correlative research purposes; Note: the goals of this study include assessment of the biologic effects of the agent being tested and are, therefore, contingent upon availability of the biologic specimens * Women of childbearing potential only: negative (serum) pregnancy test done =\< 7 days prior to registration Exclusion Criteria: * Known standard therapy for the patient's disease that is potentially curative or definitely capable of extending life expectancy * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Any of the following prior therapies: * Chemotherapy =\< 28 days prior to registration * Mitomycin C/nitrosoureas =\< 42 days prior to registration * Immunotherapy =\< 28 days prior to registration * Biologic therapy =\< 28 days prior to registration * Radiation therapy =\< 28 days prior to registration * Radiation to \> 25% of bone marrow * Bevacizumab =\< 28 days prior to registration * Failure to fully recover from acute, reversible effects of prior chemotherapy regardless of interval since last treatment * New York Heart Association classification III or IV * Known central nervous system (CNS) metastases or seizure disorder; patients with known brain metastases that have been successfully treated and stable for \>= 6 months without requirement for corticosteroids and without seizure activity will be eligible * Patients with known diabetes mellitus unless well-controlled (fasting blood sugar \[FBS\] =\< 126mg/dL and hemoglobin \[Hb\]A1C =\< 7.0) * Receiving therapeutic anticoagulation with warfarin; NOTE: prophylactic anticoagulation (i.e., low dose warfarin) of venous or arterial access devices is allowed, provided that International Normalized Ratio (INR) \< 1.5; therapeutic anti-coagulation with low molecular weight heparin is allowed at time of registration * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown: - Pregnant women - Nursing women - Men or women of childbearing potential who are unwilling to employ adequate contraception - Other concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary therapy considered investigational (utilized for a non-Food and Drug Administration \[FDA\] approved indication and in the context of a research investigation) * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * Immunocompromised patients (other than that related to the use of corticosteroids) including patients known to be human immunodeficiency virus (HIV) positive * Receiving any other investigational agent which would be considered as a treatment for the primary neoplasm * Cohort II Only: other active malignancy =\< 5 years prior to registration; EXCEPTIONS: non-melanotic skin cancer or carcinoma-in-situ of the cervix; NOTE: If there is a history or prior malignancy, patient must not be receiving other cytotoxic or molecularly targeted therapeutics treatment for their cancer; patients receiving certain hormonal manipulations as part of their treatment may be allowed to continue at the discretion of the principal investigator (PI) (e.g. luteinizing hormone-releasing hormone \[LHRH\] analogs for prostate cancer); concurrent endocrine therapy for breast cancer will not be permitted * History of myocardial infarction =\< 168 days (6 months) or congestive heart failure requiring use of ongoing maintenance therapy for life threatening ventricular arrhythmias * Known allergy to ATM (Aurothiomalate \[gold sodium thiomalate\]) or other gold compounds * \>= Grade 2 hypertriglyceridemia * \>= Grade 2 hypercholesterolemia