Lenalidomide and Doxorubicin Hydrochloride Liposome in Recurrent Ovarian Epithelial Cancer, Fallopian Tube Cancer, or Primary Peritoneal Cancer

Inclusion Criteria: * Histological diagnosis of epithelial ovarian cancer, fallopian tube cancer, or primary peritoneal cancer which has recurred or is resistant to prior treatment with at least one platinum based regimen and meeting at least one of the following criteria: * Platinum refractory - progression during the first six cycles of first line therapy with a platinum based regimen * Platinum resistant - progression within 6 months of completing first line platinum based chemotherapy * Platinum sensitive - progression more than 6 months of completing first line platinum based chemotherapy * Disease that has progressed while receiving or recurred within 6 months of completing platinum based second-line therapy Patients who have failed a second line therapy more than 6 months after completing treatment or have had more than 2 prior chemotherapy regimens will not be eligible for this study. * Measurable disease per Response Evaluation Criteria In Solid Tumors (RECIST) criteria defined as one or more lesions that can be accurately measured in at least one dimension (longest diameter to be recorded) as \> or = 20 mm with conventional techniques (CT, PET/CT, MRI, X-ray) or as \> or = 10 mm with spiral CT scan. Patients entering the study during the dose escalation component who do not meet the measurable disease requirement may enter with elevated CA 125 levels only if previously normal or stable CA 125 levels are documented after the completion of the prior chemotherapy regimen. * Age \> or = 18 years at the time of signing of consent form * Gynecologic Oncology Group (GOG) performance status of \< or = 2 * Laboratory test results within these ranges within 14 days prior to study registration: * Absolute neutrophil count \> or = 1.5 x 10\^9/L * Platelet count \> or = 100 x 10\^9/L * Serum creatinine \< or = 1.5 mg/dL * Total bilirubin \< 1.2 mg/dL * AST (SGOT) and ALT (SGPT) \< or = 2 x upper limit of institutional normal (ULN) or \< or = 5 x ULN if hepatic metastases are present. * The left ventricular ejection fraction must be at or above the lower institutional limits of normal (as assessed by MUGA scan or echocardiogram) obtained within 28 days prior to registration. * Peripheral neuropathy ≤ grade 2 (CTCAE v 3.0). * Patients who are taking a stable or decreasing dose of concomitant systemic steroids during the study must agree to also take low dose aspirin and/or other platelet-active, anti-thrombotic medication (medication\[s\] used will be decided by the Investigator) while receiving study drug and for 30 days after study drug is discontinued. * All previous cancer therapy, including chemotherapy, hormonal therapy and surgery, must have been discontinued at least 28 days prior to treatment in this study. Use of thalidomide, or structurally related compounds, radiation, or biologic response modifiers must be discontinued at least 2 weeks prior to treatment in this study. * Progression free of prior malignancies for \> or = 5 years with exception of currently treated basal cell, squamous cell carcinoma of the skin, or carcinoma "in situ" of the cervix or breast. * Females of childbearing potential (FCBP)† must have a negative serum or urine pregnancy test with a sensitivity of at least 50 mIU/mL within 10 - 14 days prior to and again within 24 hours of starting lenalidomide and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME, at least 28 days before she starts taking lenalidomide. FCBP must also agree to ongoing pregnancy testing. All patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure. * Able to take aspirin (81 or 325 mg) daily as prophylactic anticoagulation (patients intolerant to ASA may use warfarin or low molecular weight heparin) * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care. * A female of childbearing potential is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months). Exclusion criteria: * Histologic diagnosis of borderline or low malignant potential epithelial carcinoma. * Any serious medical condition, laboratory abnormality, or psychiatric illness that, in the opinion of the investigator, would prevent the patient from signing the consent form. * Prior history of myocardial infarction, congestive heart failure, or arrhythmia requiring medication. History of uncontrolled hypertension. History of systolic or diastolic dysfunction. EKG evidence of ventricular hypertrophy, conduction abnormality, or serious arrhythmia. * History of deep vein thromboembolism (DVT) within the previous 6 months, history of thrombocytopenia or bleeding disorders. * Pregnant or breast feeding females. Lenalidomide is pregnancy category X. * Any condition, including the presence of laboratory abnormalities, which places the patient at unacceptable risk if she were to participate in the study or confounds the ability to interpret data from the study. * Use of any other experimental drug or therapy within 28 days of study registration. * Known hypersensitivity reaction \> grade 2 to thalidomide or structurally related compounds * The development of erythema nodosum if characterized by a desquamating rash while taking thalidomide or similar drugs * Any prior use of lenalidomide or liposomal doxorubicin * Concurrent use of other anti-cancer agents or treatments * Known positive for HIV or infectious hepatitis, type A, B or C * Uncontrolled hyper- or hypo- calcemia, glycosemia or thyroidism