JNJ-24681585 is a histone deacetylase (HDAC) inhibitor. It is a drug in development for treatment of cancer. In this study, the safety (the effect on the body) of the drug in patients with advanced or refractory solid malignancies or lymphoma will be studied. The maximum dose that can be tolerated by patients will be determined. The absorption, break down, and elimination of the drug will be studied and in some patients the effect of food on these processes will be examined. Antitumor activity of JNJ-26481585 will be evaluated.