Docetaxel and Bortezomib in Treating Patients With Progressive or Recurrent Non-Small Cell Lung Cancer

Criteria: * No other prior malignancy except adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer for which the patient is currently in complete remission, or any other cancer for which the patient has been disease-free for 5 years. * Histologically or cytologically confirmed non-small cell lung cancer (NSCLC). * Progressive or recurrent NSCLC after treatment with 1 prior platinum-based chemotherapy regimen for metastatic disease. Prior neoadjuvant/adjuvant chemotherapy and/or concurrent chemoradiation for early-stage disease allowed. * At least 4 weeks since prior chemotherapy (6 weeks for mitomycin C or nitrosoureas) and recovered. * No prior docetaxel or bortezomib * Prior epidermal growth factor receptor inhibitor therapy allowed. * Prior paclitaxel allowed * At least 4 weeks since prior major surgery and recovered. * At least 2 weeks since prior and no concurrent enzyme-inducing anticonvulsants. * No concurrent hormonal therapy, biologic therapy, or radiotherapy to measurable lesions. Concurrent palliative radiotherapy to small-field nonindicator lesions (e.g., painful bony metastases) allowed. * Measurable disease\* with \>= 1 unidimensionally objectively measurable lesion, including any of the following: * Lung mass (measurable on chest x-ray, tomograms, or CT scan) * Enlarged lymph nodes * Liver metastasis (measurable as a discrete focal lesion on radionuclide or CT scan, or ultrasound) * Metastatic abdominal mass (measurable on CT scan with \>= 1 perpendicular diameter ≥ the distance between cuts) * Measurable disease must be outside the previous radiation field or a new lesion must be present. * Life expectancy \>= 12 weeks * Progressive disease within a previously radiated field allowed. * \[Note: \*Measurable disease DOES NOT include bone metastases or non-focal liver metastases\]. * No symptomatic or untreated brain metastasis requiring steroids. Asymptomatic, previously treated (surgical resection or radiotherapy) brain metastasis allowed provided they are neurologically stable and \>= 4 weeks since prior steroids. * Creatinine clearance \>= 50 mL/min * Creatinine =\< 1.6 mg/dL * Bilirubin normal * AST =\< 2 times upper limit of normal * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No peripheral neuropathy \>= grade 2 * Absolute granulocyte count \>= 1,500/mm³ * Platelet count \>= 100,000/mm³ * Cutaneous nodule * ECOG performance status 0-1 * At least 4 weeks since prior radiotherapy and recovered.