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 before beginning therapy on this protocol) are excluded from this study * Peripheral neuropathy of severity greater than grade 1 * Known history of allergic reactions to paclitaxel * Prior therapy with paclitaxel * Inability to take oral medications on a continuous basis; patients unable to swallow the vorinostat capsules whole are ineligible (the capsules cannot be crushed or broken) * 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 * Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with vorinostat; women of childbearing potential must use an appropriate double barrier method of birth control (such as female use of a diaphragm, intrauterine device \[IUD\], sponge and spermicide, in addition to the male use of a condom) or a prescribed birth control implant or practice abstinence; both double barrier contraception and implants must be used for at least one week prior to the start of the research study and continue for at least two weeks following the last study visit; please note that birth control pills should not be used while on this study as they may have a negative interaction with the experimental drug in this study * HIV-positive patients receiving combination antiretroviral therapy are ineligible