Carboplatin and Paclitaxel With or Without Vorinostat in Treating Patients With Advanced Non-Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically confirmed non-small cell lung cancer * No prior chemotherapy for advanced or metastatic disease * ECOG performance status 0 or 1 * Patients must have measurable disease, 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 * Life expectancy of greater than 12 weeks * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin within normal institutional limits * AST(SGOT)/ALT(SGPT) =\< 2.5 x institutional upper limit of normal * Creatinine within normal institutional limits OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy in a metastatic setting * Patients may not be receiving any other investigational agents * Patients with untreated brain metastases should be excluded from this clinical trial; however, patients who have stable brain disease (should be off corticosteroids) at least 3 weeks after completion of appropriate therapy are eligible * Patients who have received any prior HDAC inhibitor (except valproic acid for seizure control provided that the valproic acid has been stopped at least 30 days …