Phase II MOR00208 in Combination With Lenalidomide for Patients With Relapsed or Refractory CLL, SLL or PLL or Older Patients With Untreated CLL, SLL or PLL

Inclusion Criteria: * Patients with a diagnosis of intermediate or high risk CLL, SLL, or B cell (B)-PLL by Biennial International Workshop on CLL (IWCLL) 2008 criteria who have * COHORT 1: previously untreated disease AND refuse or are ineligible for approved chemo- and/or -immunotherapy options for untreated CLL/SLL/PLL * COHORT 2: previously received at least one therapy for their disease * All patients must satisfy one of the following criteria for active disease requiring therapy: * Evidence of marrow failure as manifested by the development or worsening of anemia or thrombocytopenia (not attributable to autoimmune hemolytic anemia or thrombocytopenia) * Massive (\>= 6 cm below the costal margin), progressive or symptomatic splenomegaly * Massive nodes (\>= 10 cm) or progressive or symptomatic lymphadenopathy * Constitutional symptoms, which include any of the following: * Unintentional weight loss of 10% or more within 6 months * Significant fatigue limiting activity * Fevers \>= 100.5 degrees Fahrenheit (F) for 2 weeks or more without evidence of infection * Night sweats \> 1 month without evidence of infection * Patients with a history of Richter's transformation are eligible if they now have evidence of CLL only, with \< 10% large cells in the bone marrow * Creatinine =\< 2 * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) \< 2.5 x upper limit of normal * Bilirubin =\< 2 times the upper limit of normal, unless relat…