The study will be a dose-finding, phase I study of the combination of vorinostat and PLD in patients with advanced lymphoma refractory to at least one prior systemic therapy. The study will also be a dose-escalating study of vorinostat 200mg to 400 mg twice daily for 7 days with PLD 30mg/m2 on day 3 every 21 days, with intrapatient dose escalation.