FDG-Labeled PET Scan in Planning Chemotherapy in Treating Patients With Stage IIIB or IV Non-Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically confirmed NSCLC; patients must have stage IIIB with malignant pleural effusion or with nodal disease so extensive that it is not amenable to radiotherapy with curative intent, or stage IV disease, as defined by the American Joint Committee on Cancer (AJCC) cancer staging handbook, 6th Edition (2002) * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (\>= 10 mm with spiral CT scan); patients' baseline FDG-PET scan must demonstrate a target lesion with SUV \>= 2 x background and SUV \> 3 * All patients must not have received treatment with conventional cytotoxic chemotherapy for NSCLC; patients may have had prior radiotherapy or may have been treated with the epidermal growth factor receptor (EGFR) tyrosine kinase inhibitors (TKI) (i.e. erlotinib or gefitinib); one week must have elapsed after discontinuation, prior to the initial PET scan for patients previously treated with a TKI; patients who receive radiotherapy must have recovered from the side effects of therapy (except alopecia) and have measurable disease (target lesion) outside of the radiation field * Life expectancy \>= 3 months * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< 1.5 x institutional upper limit of normal (ULN) * Aspartate aminotransferase (AST)(serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT)(serum glutamic pyruvic transaminase \[SGPT\]) =\< 2 x institutional ULN (\< 5 x ULN for patients with liver metastases) * Creatinine =\< 1.5 x ULN OR creatinine clearance \>= 40 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Patients must have baseline FDG-PET and CT scans performed at the University of Washington (UW)/Seattle Cancer Care Alliance (SCCA) within two weeks from the start of chemotherapy * Asymptomatic patients with clinically stable brain metastases (treated or untreated) are allowed * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) throughout treatment and for 30 days following the last dose of chemotherapy * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have received EGFR TKI (i.e. erlotinib or gefitinib) within one week 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 agents used in the study * Inability or unwillingness to take corticosteroids, which are required pre-medications for the chemotherapies in this trial * Diabetes requiring insulin for management * Patients must weigh less than 400 lbs * Patients with post-obstructive pneumonia or lobar collapse * Significant neuropathy (common toxicity criteria \[CTC\] grade \> 2), as both the paclitaxel and docetaxel have potential for neurotoxicity * 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 or breastfeeding women * Patients with a detectable second malignancy are excluded, as this could confound tumor evaluation and affect patient survival * Patients who are likely to need palliative radiation therapy for painful bony metastases, impending fractures, or hemoptysis