Exemestane, Pemetrexed Disodium, and Carboplatin in Treating Post-Menopausal Women With Stage IV Non-Small Cell Lung Cancer

Inclusion Criteria: * Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information (PHI) * Histologically or cytologically confirmed, treatment-naive (or status post a single treatment regimen of a tyrosine kinase inhibitor as a single agent) stage IV non-squamous, NSCLC * Measurable disease according to modified RECIST version 1.1 * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Expected survival time of \>= 3 months in the opinion of the investigator * Postmenopausal women; women are eligible if they are postmenopausal (older than 50 years of age with no spontaneous menses for at least 12 months; or 50 years of age or younger either with no spontaneous menses \[amenorrheic\] within 12 months of randomization \[e.g., spontaneous or secondary to hysterectomy\] and a follicle-stimulating hormone level within the postmenopausal range or with prior bilateral oophorectomy) * Ability to provide a formalin-fixed, paraffin-embedded (FFPE) tumor tissue sample containing representative tumor tissue from a previously obtained biopsy/resection that meets specific tissue sample requirements at screening Exclusion Criteria: * History of another primary cancer within 3 years prior to day 1 with the exception of curatively treated skin cancer (other than melanoma) or curatively treated cervical carcinoma in-situ * Untreated central nervous system (CNS) involvement; (treated CNS involvement is permitted only if the patient is not currently on steroid therapy or has remained on a stable, unchanged dose of steroid for \>= 3 weeks) * Recent major surgery within the prior 4 weeks; (mediastinoscopy or placement of a central venous access will be allowed as long as placement was more than 7 days prior to receiving study drug) * Any prior or concurrent investigational or standard therapy for treatment of metastatic NSCLC including radiation therapy, chemotherapy, biological therapy (with the exception of a single treatment regimen of a tyrosine kinase inhibitor as a single agent, which must be completed 28 days prior to day 1), hormonal therapy, or immunotherapy; (palliative-targeted radiotherapy for brain or bone metastases is permitted providing it has been at least 14 days prior to day 1) * History of hormone replacement therapy (estrogens with or without progestin) or an aromatase inhibitor (anastrazole, letrozole, exemestane) within 8 weeks prior to day 1 * Osteoporosis complicated by pathologic fracture * Concurrent investigational agents for non-malignant disease or prior investigational agents for non-malignant disease within 4 weeks or 5 half-lives (whichever is shorter) prior to day 1 * Concurrent cytotoxic or immunosuppressive therapy for non-malignant disease (e.g., for rheumatoid arthritis or lupus) * Absolute neutrophil count (ANC) \< 1500/mL * Platelet count \< 100,000/mL * Hemoglobin \< 9.0 g/dL * Serum bilirubin \> 1.5 x upper limits of normal (ULN) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \> 2.5 x ULN (AST and ALT \> 5 x ULN for subjects with liver metastasis) * Glomerular filtration rate (GFR) =\< 50 * Albumin =\< 2.5 g/dL * Known history of or positive test result for human immunodeficiency virus (HIV) * Active infection (including HIV/acquired immune deficiency syndrome \[AIDS\], hepatitis B, or hepatitis C infection) requiring systemic antibiotics, antivirals, or antifungals * History of myocardial infarction within 12 months prior to day 1 or clinically significant coronary disease * New York Heart Association grade II or greater congestive heart failure * Unstable coronary disease or clinically significant electrocardiogram (ECG) (12-lead) abnormalities, as determined by the investigator * Inability to comply with study and follow-up procedures * Any other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding that leads to reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results or render the subject at high risk from treatment complications * Other unspecified reasons that, in the opinion of the investigator or sponsor, make the subject unsuitable for enrollment