Imatinib Mesylate and Paclitaxel in Treating Older Patients With Stage IIIB or Stage IV Non-Small Cell Lung Cancer

Inclusion Criteria: * Histologic or cytologic diagnosis of non-small cell lung cancer * At least one site of measurable disease, as defined by the modified RECIST criteria * Stage IIIB with pleural effusion or Stage IV disease; includes patients who received surgery alone for early stage disease, now in relapse with advanced disease; staging is according to the American Joint Committee on Cancer classification scheme, 6th edition * Total bilirubin \< 1.25 x upper limit of normal (ULN) * Baseline absolute neutrophil count \>= 1500/uL * Baseline platelet count \>= 100,000/uL * ECOG Performance Status 0, 1 or 2 at the time of informed consent * Written, voluntary consent * Patients with reproductive potential must use an acceptable contraceptive method, such methods include: 1) Male hormonal contraception; 2) Partner without reproductive potential, including post-menopausal status or history of tubal ligation; 3) Partner with intrauterine device (IUD) or contraceptive vaginal ring; 4) Partner takes oral contraceptive pill, wears contraceptive patch, or has contraceptive implant; 5) Routine use of barrier method, such as condoms or diaphragm, during sexual intercourse * AST and ALT =\< 2.5 x ULN * Creatinine =\< 1.5 x ULN Exclusion Criteria: * Uncontrolled brain metastasis; patients with known brain metastasis must have completed treatment with surgery, radiation or both; in addition, they must be off corticosteroids * Symptomatic neuropathy (Grade 2 or higher) * Prior chemotherapy for advanced non-small cell lung cancer (Prior adjuvant, neoadjuvant, or chemoradiotherapy for NSCLC is permitted, provided at least 6 months elapsed prior to documented metastatic recurrence) * Patient is \< 5 years free of another primary malignancy, except: a) if the other malignancy is basal cell carcinoma or cervical carcinoma in situ or b) if the other primary malignancy is not considered clinically significant and is requiring no active intervention * Prior radiation therapy to \> 25% of bone marrow * Grade III/IV congestive heart failure, as defined by NYHA criteria, or myocardial infarction within 6 months * Any serious or uncontrolled concomitant disorder that, in the opinion of the investigator, would compromise the patient's ability to complete the study * Patient has known chronic liver disease, e.g., diagnosis of chronic active hepatitis or cirrhosis * Major surgery two weeks prior to study treatment * Patient with any significant history of non-compliance to medical regimens or with inability to grant reliable informed consent * Any condition requiring continuous administration of systemic corticosteroids * The patient is on therapeutic anti-coagulation with warfarin * The administration of any other anticancer agents including chemotherapy and biologic agents is NOT permitted * The use of other concurrent investigational drugs is not allowed * Participants in this study must avoid grapefruit juice or other grapefruit-containing products for the duration of treatment with imatinib