This is a phase III open label clinical trial to evaluate the long-term efficacy and safety of lomitapide at the maximum tolerated dose (for each patient) established during the clinical trial 733-005/UP1002. Subjects completing study 733-005/UP1002 who have not met any of the stopping criteria will be eligible to participate in 733-012. The treatment period will continue until a decision has been made by the local competent authority regarding marketing authorization. Lomitapide will be given orally once daily. Patient specific doses will be carried forward from 733-005/UP1002, but will not exceed the maximum tolerated dose the patient received during 733-005 /UP1002. The maximum dose for any patient is 80 mg/day. There is no reference therapy in this trial. The effects of the study drug will be compared to baseline data (from 733-005/UP1002). Concomitant lipid-lowering therapy including plasmapheresis or LDL apheresis is permitted.