A Phase I Trial of SS1 (dsFv) PE38 With Paclitaxel, Carboplatin, and Bevacizumab in Subjects With Unresectable Non-Small Cell Lung Adenocarcinoma

Background: * Advanced cases of non-small-cell lung carcinoma (NSCLC) usually are not successfully treated with standard therapies. Even treatments that attempt to specifically target NSCLC cells have not proved effective. * Researchers are interested in determining whether a combination of the chemotherapy drugs SS1 (dsFv) PE38, paclitaxel, carboplatin, and bevacizumab may be effective in shrinking the size of NSCLC tumors. Three of the drugs (paclitaxel, carboplatin, and bevacizumab) are commercially available, while the other is a drug that is currently being tested to determine its usefulness in cancer treatment. This study will help to determine if the combination of all four drugs is more effective and as safe, safer, or less safe than other drug combinations given to treat NSCLC. Objectives: \- To determine a safe and tolerable dose for the combination of SS1 (dsFv) PE38 with paclitaxel, carboplatin, and bevacizumab in patients with advanced mesothelin-expressing lung adenocarcinoma. Eligibility: * Age \> 18 years of age * Newly diagnosed advanced non-small-cell lung carcinoma * No prior chemotherapy for lung cancer * Individuals at least 18 years of age who have advanced non-small-cell lung carcinoma that has not responded to standard treatments. Design: * The study will last for two 21-day cycles of treatment for the four-drug combination, with additional treatment cycles of carboplatin, paclitaxel, and bevacizumab. * Two to three weeks prior to the study, participants will be screened with a full medical history and physical exam, bone marrow biopsy (we do not do bone marrow biopsies) (if one has not been performed in the last 6 months), computed tomography (CT) or ultrasound scan, tumor measurements, and other tests as required by the researchers. Participants will provide blood and urine samples at this time as well. * During the study, participants will receive SS1 (dsFv) PE38, carboplatin, paclitaxel, and bevacizumab for a maximum of two cycles.