Lenalidomide in Combination With a Fixed Dose of Sorafenib for the Treatment of Hepatocellular Carcinoma

Inclusion Criteria: * Clinical or pathological diagnosis of unresectable hepatocellular carcinoma (HCC) based on radiologic criteria, elevated alpha fetoprotein and/or tissue biopsy * All previous cancer therapy, including radiation, hormonal therapy and surgery, must have been discontinued at least 28 days prior to treatment in this study * Child-Pugh Liver Function Class A/B9 * Eastern Cooperative Oncology Group (ECOG) performance status of \</= 2 at study entry * Laboratory test results within protocol-specific ranges * Disease free of prior malignancies for \>/= 5 years with exception of currently treated basal cell, squamous cell carcinoma of the skin, or carcinoma "in situ" of the cervix or breast. * All study participants must be registered into the mandatory RevAssist® program, and be willing and able to comply with the requirements of RevAssist® (Revlimid is only available under a restricted distribution program called "RevAssist.") * Females of childbearing potential must have two negative pregnancy tests before starting lenalidomide and must agree to use two methods of birth control and submit to pregnancy tests throughout the study. * Able to take aspirin daily as prophylactic anticoagulation * Age \>18 years at the time of signing the informed consent form * Life expectancy of at least 30 days Exclusion Criteria: * No serious medical condition, laboratory abnormality, or psychiatric illness (including no evidence of hepatic encephalopathy) that would prevent the subject from signing the informed consent form * No pregnant or breast feeding females. (Lactating females must agree not to breast feed while taking lenalidomide) * No patients who have undergone surgical resection or received chemotherapy, percutaneous ethanol injection, radiation therapy or chemoembolization within 30 days prior to commencement of the study * No condition, including the presence of laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study * No use of any other experimental drug or therapy within 28 days of baseline * No known hypersensitivity to thalidomide * Patients who developed erythema nodosum if characterized by a desquamating rash while taking thalidomide or similar drugs will be excluded * No prior use of lenalidomide * No concurrent use of other anti-cancer agents or treatments * No known positivity for HIV or infectious hepatitis, type B-8/9 or C * No active infection not controlled effectively with antimicrobial or antiviral therapy