Suberoylanilide Hydroxamic Acid in Treating Patients With Stage IIIB, Stage IV, or Recurrent Non-Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed non-small cell lung carcinoma, Stage IV (distant metastases), stage IIIB with malignant pleural effusion, or recurrent disease * 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 * Prior therapy: no more than 1 prior cytotoxic chemotherapy regimen for their Stage IIIB/IV or recurrent disease; no previous irradiation to the only area of measurable disease, unless that site had subsequent progression of disease; radiation therapy must be completed at least 3 weeks prior to initiating study drug * Stage IV patients with brain metastases are eligible providing the brain metastases are clinically and radiologically stable 4 weeks after treatment with surgery and/or radiation therapy, and they are not taking steroids * Life expectancy greater than 3 months * ECOG performance status 0 or 1 (Karnofsky \>= 70%) * Patients must have normal organ and marrow function as defined below: * 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 * Peripheral neuropathy =\< grade 1 * Caution needs to be exercised when using SAHA with medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of SAHA; since grapefruit juice is known to interact with the CYP450 enzymes, it is recommended that patients abstain from consuming grapefruit, grapefruit juice, and other grapefruit containing products during this study * The effects of SAHA on the developing human fetus at the recommended therapeutic dose are unknown; for this reason and because HDAC inhibitors are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document * Patients should not have taken valproic acid, another histone deacetylase inhibitor, for at least 2 weeks prior to enrollment Exclusion Criteria: * Patients who have had chemotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) or radiotherapy within 3 weeks prior to entering the study * Patients may not be receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to SAHA * Any other active malignancy in the past 5 years except non-melanoma skin cancers * 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 * Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with SAHA, breastfeeding should be discontinued if the mother is treated with SAHA * HIV-positive patients receiving combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with SAHA; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated