This phase II trial will address the issues of bevacizumab treatment duration and treatment safety by incorporating bevacizumab into a variation of the ECOG reference regimen as first-line therapy for patients with non-squamous non-small cell lung cancer. Following disease progression or treatment failure, the potential benefit of continued bevacizumab therapy will be tested by randomizing patients to two treatment arms, including second-line chemotherapy with or without further bevacizumab.