The purpose of this phase I study of oral panobinostat plus cisplatin and pemetrexed is to determine the maximum tolerated dose (MTD) and dose limiting toxicities (DLTs) in patients with advanced solid tumors, with an emphasis in non-small cell lung cancer. Another purpose of this study is to find out if oral panobinostat in combination with cisplatin and pemetrexed can be administered safely without significant increase in toxicity and that the combination will increase efficacy compared to platinum-based doublet chemotherapy alone.