Gemcitabine, Carboplatin, and Bortezomib in Advanced or Recurrent Non-Small Cell Lung Cancer

Inclusion Criteria: * Patients must have histologically or cytologically proven selected stage IIIB (T4 lesion due to malignant pleural effusion) or stage IV, advanced non-small cell lung cancer or recurrent disease after previous surgery and/or radiation * Patients with known brain metastases are not eligible for this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events; all patients must have a pretreatment CT or MRI scan of the brain to evaluate for CNS disease within 28 days prior to registration * Patients must have measurable OR non-measurable disease documented by CT, MRI, or x-ray; measurable disease must be assessed within 28 days prior to registration and non-measurable disease must be assessed within 42 days prior to registration; pleural effusions, ascites and laboratory parameters are not acceptable as the only evidence of disease * Patients must not have received any prior systemic chemotherapy or biological agent for non-small cell lung cancer; prior radiation is permitted; however, two weeks must have elapsed since the completion of prior radiation therapy and patients must have recovered from all associated toxicities at the time of registration; measurable or non-measurable disease must be outside the previous radiation field or a new lesion inside the port must be present * At least two weeks must have elapsed since surgery (thoracic or other major surgeries) and patients must have recovered from all associated toxicities at the time of registration * Serum creatinine =\< the institutional upper limit of normal OR a creatinine clearance \>= 60 cc/min; these tests must have been performed within 28 days prior to registration * ANC \>= 1500/ul obtained within 14 days prior to registration * Platelet count \>= 100,000/ul obtained within 14 days prior to registration * Serum bilirubin =\< institutional upper limit of normal obtained within 28 days prior to registration * SGOT or SGPT =\< 2.5 x the institutional upper limit of normal obtained within 28 days prior to registration * All patients must have a Zubrod performance status of 0-1 * Peripheral neuropathy, if present, must be =\< grade 1 (NCI Common Terminology Criteria for Adverse Events version 3.0) * Correlative science studies: Institutions must have IRB approval of S9925 (the Lung Cancer Specimen Repository); patients must be offered participation in S9925; with the patient's consent, tumor tissue, blood and plasma will be submitted for testing via S9925; patients must be registered separately to S9925 in order for institutions to receive credit for specimen submissions * Patients known to be HIV positive and receiving anti-retroviral therapy (HAART) are not eligible for this study because of possible pharmacokinetic interactions * Patients must not be planning to receive any other concomitant anticancer treatment including chemotherapy, radiation therapy, biologic agents or any other investigational drugs * Patients should not have known hypersensitivity to boron, mannitol, or PS-341; if day 28 or 42 falls on a weekend or holiday, the limit may be extended to the next working day; in calculating days of tests and measurements, the day a test or measurement is done is considered day 0; therefore, if a test is done on a Monday, the Monday four weeks later would be considered day 28; this allows for efficient patient scheduling without exceeding the guidelines * No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission or other cancer from which the patient has been disease-free for 5 years * Pregnant or nursing women may not participate in this trial because of the increased risk of fetal harm including fetal death from the chemotherapeutic agents; women/men of reproductive potential may not participate unless they have agreed to use an effective contraceptive method * Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines * At the time of patient registration, the treating institution's name and ID number must be provided to the Data Operations Center in Seattle in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered into the data base