Vorinostat, Paclitaxel, and Radiation Therapy in Treating Patients Unable to Tolerate Cisplatin With Stage III Non-Small Lung Cancer That Cannot Be Removed By Surgery

Inclusion Criteria: * Histologically or cytologically proven diagnosis of NSCLC * Inoperable Stage IIIA or IIIB (excluding malignant pleural effusion) disease according to the American Joint Committee on Cancer (AJCC) Cancer Staging Manual, Sixth edition (2002) * At least one site of measurable disease, as defined by the modified Response Evaluation Criteria In Solid Tumors (RECIST) criteria * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Inability to tolerate full dose cisplatin as defined by: * Creatinine clearance less than 50ml/min * Greater than grade 2 sensory hearing loss (as defined by National Cancer Institute \[NCI\] Common Terminology Criteria for Adverse Events \[CTCAE\] criteria v3.0 adverse event term "Hearing: Patients without baseline audiogram and not enrolled in a monitoring program") * Performance status \>= 2 * Age \>= 75 years * Cardiac history, such as myocardial infarction within 6 months, angina, or heart disease as defined by the New York Heart Association (NYHA) Class III or IV * Any other comorbid disease or condition that would increase the risk of toxicity of cisplatin therapy * Female patient is either post menopausal, free from menses for \>= 2 years, surgically sterilized or willing to use 2 adequate barrier methods of contraception to prevent pregnancy or agrees to abstain from heterosexual activity throughout the study * Female patient of childbearing potential has a negative serum pregnancy test beta-human chorionic gonadotropin (hCG) within 7 days prior to receiving the first dose of vorinostat * Male patient agrees to use an adequate method of contraception for the duration of the study * Absolute neutrophil count (ANC) \>= 1,500/mcL * Platelets \>= 100,000/mcL * Hemoglobin \>= 9 g/dL * Prothrombin Time or International Normalized Ratio (INR) =\< 1.5x upper limit of normal (ULN) unless receiving therapeutic anticoagulation * Partial thromboplastin time (PTT) =\< 1.2 times the ULN unless the patient is receiving therapeutic anticoagulation * Potassium levels: Normal limits * Magnesium levels: Normal limits * Calculated creatinine clearance \>= 20 mL/min * Serum total bilirubin =\< 1.5 X ULN * Aspartate aminotransferase (AST) (serum glutamate oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X ULN * Alkaline Phosphatase =\< 2.5 X ULN * Patient, or the patient's legal representative, has voluntarily agreed to participate by giving written informed consent * Patient has a life expectancy of at least 12 weeks * Patient is available for periodic blood sampling, study related assessments, and management at the treating institution for the duration of the study Exclusion Criteria: * Patient who has had chemotherapy, radiotherapy, or biological therapy for NSCLC within 5 years prior to initial dosing with study drug(s) * Symptomatic neuropathy (\>= grade 2) * Patient is currently participating or has participated in a study with an investigational compound or device within 30 days of initial dosing with study drug(s) * Patient had prior treatment with an histone deacetylases (HDAC) inhibitor (e.g., romidespsin \[Depsipeptide, NSC-630176\], entinostat \[MS 275\], dacinostat \[LAQ-824\], belinostat \[(PXD-101\]), panobinostat \[LBH589\], mocetinostat \[MGCD0103\], CRA024781, etc); patients who have received compounds with HDAC inhibitor-like activity, such as valproic acid, as anti-tumor therapy should not enroll in this study; patients who have received such compounds for other indications, e.g., valproic acid for epilepsy, may enroll after a 30-day washout period * Patient has known hypersensitivity to the components of study drug or its analogs or paclitaxel * NYHA Class III or IV congestive heart failure, myocardial infarction within the previous 6 months, QTc \> 0.47 seconds, or uncontrolled arrhythmia * Patient is pregnant or breast feeding, or expecting to conceive or father children within the projected duration of the study * Patient with a "currently active" second malignancy, other than non-melanoma skin cancer and carcinoma in situ of the cervix, should not be enrolled; patients are not considered to have a "currently active" malignancy if they have completed therapy for a prior malignancy, are disease free from prior malignancies for \> 5 years or are considered by their physician to be at less than 30% risk of relapse * Patient has a history or current evidence of any condition, therapy, or lab abnormality that might confound the results of the study, interfere with the patient's participation for the full duration of the study or is not in the best interest of the patient to participate