R-ICE and Lenalidomide in Treating Patients With First-Relapse/Primary Refractory Diffuse Large B-Cell Lymphoma

Inclusion Criteria: * Age \>= 18 years * Phase I: Histological confirmation of expressing CD20 antigen as determined by pathology at the respective institution and central pathology review at Mayo Clinic Rochester; all types of B-cell lymphomas are allowed to participate; patients with primary mediastinal large B-cell (PMLBCL) or transformed lymphoma are allowed to participate * Phase II: Histological confirmation of DLBCL expressing CD20 antigen as determined by pathology at the respective institution and central pathology review at Mayo Clinic Rochester; patients with primary mediastinal large B-cell (PMLBCL) or transformed lymphoma are not allowed to participate * Measurable disease (at least 1 lesion \>= 1.5 cm in diameter) as detected by PET/CT * Only 1 line of previous anti-lymphoma therapy is allowed and not currently receiving any other agent that would be considered as a treatment for the lymphoma; patients must be \>= 2 weeks from prior anti-lymphoma therapy; the use of steroids and/or rituximab up to 1 week prior to registration for management of symptoms is allowed * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-2 * Absolute neutrophil count (ANC) \>= 1500/mm\^3, obtained =\< 7 days prior to registration * Platelet count \>= 75,000/mm\^3, obtained =\< 7 days prior to registration * Total bilirubin =\< 2 x upper limit of normal (ULN) (unless related to lymphoma or Gilbert's disease) OR =\< 5 x ULN for subjects with documented or suspected Gil…