The main goal during the Phase I portion of this research study is to find out the highest and safest dose of LBH589 that can be given in combination with carboplatin with etoposide in subjects with lung cancer without causing severe side effects. The main goal of the Phase II portion of this study is to find how the subject's lung cancer responds to the LBH589 in combination with carboplatin and etoposide at the highest and safest dose that was given in Phase I.