Fludeoxyglucose F-18 PET/CT in Predicting Response to Chemotherapy in Patients With Stage IIIA Non-small Cell Lung Cancer That Can Be Removed by Surgery

Inclusion Criteria: * Patient must have stage IIIA non-small cell lung cancer (T1-3N2) per American Joint Committee on Cancer (AJCC) 7th edition and must be considered to be surgically resectable * Patients must be assessed by surgeons and are considered surgically resectable * Mediastinal nodal metastases (N2) disease must be confirmed histologically * Easter Cooperative Oncology Group (ECOG) performance status 0 or 1 * Required imaging studies obtained within four weeks prior to registration * White blood cell (WBC) \>= 4000 mm\^3 or granulocyte count at least 2,000/mm\^3 * Platelets \>= 100,000/mm\^3 * Hemoglobin \>= 10.0g/dL * Total bilirubin \< 1.5 mg/dL * Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) \< 3 x upper limit of normal (ULN) * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) \< 3 x ULN * Alkaline phosphatase \< 3 x ULN * Calculated/estimated or measured creatinine clearance at least 50 ml/min; note: creatinine clearance should be calculated using the Cockcroft-Gault formula; patients who will receive pemetrexed/cisplatin therapy must be obtained within 2 weeks of registration * Patients cannot have hormonal cancer therapy or radiation therapy as prior cancer treatment within 5 years of registration; (prior surgery, biologic therapy, hormonal therapy, or radiation therapy for a malignancy over 5 years prior to enrollment that is not considered cured is acceptable) * Patients must not have any history of other cancer within 5 years from registration with the exception of in situ carcinoma of the cervix, in situ carcinoma of the breast or completely resected non-melanoma skin cancer * Patients may not have received prior chemotherapy or radiation therapy for lung cancer * Patients with a history of myocardial infarction are eligible if the event occurred \> 6 months prior to entry * Patients must not have any clinically significant ongoing, active or serious infection, symptomatic or uncontrolled congestive heart failure, active angina, symptomatic or uncontrolled cardiac arrhythmia or any other medical condition or psychiatric illness/social situations that would limit compliance with study requirements * Patents must have no contraindication to cisplatin chemotherapy including no clinically significant hearing loss unless willing to accept the potential of further loss of hearing, no symptomatic peripheral neuropathy * Women must not be pregnant or breast-feeding * All females of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy * A female of childbearing potential is any woman, regardless of sexual orientation or whether they have undergone tubal ligation, who meets the following criteria: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) * Women of childbearing potential and sexually active males must be strongly advised to use an accepted and effective method of contraception or to abstain from sexual intercourse for the duration of their participation in the study * Patients must not have received any study therapies prior to registration * Pemetrexed/cisplatin therapy; note: patients who will receive pemetrexed/cisplatin therapy must meet all eligibility criteria below: * Patients assigned to pemetrexed/cisplatin therapy must NOT have squamous cell histology * Calculated creatinine clearance must be obtained within 2 weeks of registration and calculated creatinine clearance (CrCl) must be \>= 45mL/min using the standard Cockcroft and Gault formula, or the measured glomerular filtration rate (GFR) using the appropriate radiolabeled method (51-CrEDTA or Tc99m-DTPA) must be used to calculate CrCl * Patients should have no contraindications for FDG-PET/CT