Inclusion Criteria:  Participants must satisfy the following criteria to be enrolled in the study:  Participant is ≥ 18 years of age at the time of signing the informed consent form (ICF).  Participant has histologically confirmed (per local evaluation) diagnosis of, aggressive B-cell lymphoma (a-BCL) according to 2016 WHO classification among the following subtypes:  Diffuse large B-cell lymphoma (DLBCL), Not otherwise specified (NOS) including Germinal center B-cell and Activated B-cell types; High-grade B-cell lymphoma, with MYC and B-cell lymphoma 2 (BCL2) and/or B-cell lymphoma 6 (BCL6) rearrangements; Primary mediastinal (thymic) large B-cell lymphoma (PMBCL); Primary cutaneous DLBCL-leg type; Anaplastic lymphoma kinase positive (ALK+) large B-cell lymphoma; Epstein Barr virus positive (EBV+) DLBCL, NOS; Grade 3b Follicular lymphoma (FL). Participants must have relapsed or refractory disease after at least 2 prior lines of therapy including Rituximab, cyclophosphamide, doxorubicin hydrochloride, vincristine sulfate, and prednisone (R-CHOP)-like regimen OR after one prior line of standard therapy and being not eligible for autologous stem cell transplant (ASCT); participants previously treated with CAR-T therapy can be enrolled. Participant must have measurable disease defined by at least one FDG-avid lesion for FDGavid-subtype and one bi-dimensionally measurable (> 1.5 cm in longest diameter) disease by computed tomography (CT) or magnetic resonance imaging (MRI), as defined by the Lugano classification (Cheson, 2014). Participant has an Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2.  Participant must have the following laboratory values:  Absolute neutrophil count (ANC) ≥ 1.5 x 109/L or ≥ 1.0 x 109/L in case of documented bone marrow involvement (> 50% or tumor cells), without growth factor support for 7 days (14 days if pegylated granulocyte-colony stimulating factor (peg-G-CSF)) Hemoglobin ≥ 8 g/dL Platelets ≥ 75 x 109/L or ≥ 50 x 109/L in case of documented bone marrow involvement (> 50% or tumor cells), without transfusion for 7 days Aspartate aminotransferase / serum glutamic oxaloacetic transaminase (AST/SGOT) and alanine aminotransferase / serum glutamic pyruvic transaminase (ALT/SGPT) ≤ 2.5 x ULN except in the case of documented liver involvement by lymphoma, where ALT/SGPT and AST/SGOT must be ≤ 5.0 x ULN. Serum total bilirubin ≤ 2.0 mg/dL (34 μmol/L) except in cases of Gilbert syndrome, then ≤ 5.0 mg/dL (86 μmol/L) Estimated serum creatinine clearance of ≥ 50 mL/minute using the modification of diet in renal disease formula.  All participants must:  Have an understanding that the study drug could have a potential teratogenic risk. Agree to follow all requirements defined in the Pregnancy Prevention Program for CC-220 Pregnancy Prevention Plan for Participants in Clinical Trials.  A female of childbearing potential (FCBP) must:  a. Have two negative pregnancy tests as verified by the investigator prior to starting study therapy. She must agree to ongoing pregnancy testing during the course of the study, and after end of study therapy.  Male participants must:  Practice true abstinence (which must be reviewed on a monthly basis and source documented) or agree to use a condom during sexual contact with a pregnant female or a female of childbearing potential while participating in the study.  Exclusion Criteria:  The presence of any of the following will exclude a participant from enrollment:  Participant has any significant medical condition, active infection (including SARS-CoV-2 suspected or confirmed), laboratory abnormality, or psychiatric illness that would prevent the participant from participating in the study.  a. In the case of prior SARS-CoV-2 infection, symptoms must have completely resolved  Participant has any condition including the presence of laboratory abnormalities, which places the participant at unacceptable risk if he/she were to participate in the study. Participant has any other subtype of lymphoma. Participant has received systemic anti-cancer treatment, CAR-T or any T-cell targeting treatment (approved or investigational) ≤ 5 half-lives or 4 weeks prior to starting CC-220, whichever is shorter. Participant has received prior therapy with a Cereblon-modulating drug (eg, lenalidomide, avadomide) ≤ 4 weeks prior to starting CC-220. Participant has persistent diarrhea or malabsorption ≥ Grade 2 (NCI-CTCAE v5.0), despite medical management. Participant has peripheral neuropathy ≥ Grade 2 (NCI CTCAE v5.0). Participant is on chronic systemic immunosuppressive therapy or corticosteroids. Participant has impaired cardiac function or clinically significant cardiac disease. Participant had major surgery ≤ 2 weeks prior to starting CC-220. Participant has known seropositivity for or active viral infection with human immunodeficiency virus (HIV). Participant has known chronic active hepatitis B  Participant has history of other malignancy, unless being free of the disease for ≥ 3 years prior to starting study drug; exceptions to the ≥ 3-year time limit include history of the following:  Localized non-melanoma skin cancer Carcinoma in situ of the cervix Carcinoma in situ of the breast Incidental histologic finding of prostate cancer (T1a or T1b as per Tumor Node Metastasis [TNM] staging system) or prostate cancer that has been treated with curative intent. Participant has current treatment with strong CYP3A4/5 modulators. Participant has known hypersensitivity to any component of planned combination medications in the regimen. Participant has known allergy to thalidomide, pomalidomide, lenalidomide or avadomide.