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 related to disease or Gilbert's disease * Platelets \>= 30 x 10\^9/L and absence of active bleeding * Absolute neutrophil count (ANC) \>= 1000/mm\^3 unless due to CLL involvement of the marrow * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Patients must not have secondary cancers that result in a life expectancy of \< 2 years or that would confound assessment of toxicity in this study * Patients must provide written informed consent; a signed copy of the consent form will be retained in the patient's chart * Patients must be able to receive outpatient treatment and follow-up at the treating institution * Patients must have completed all CLL therapies \> 4 weeks prior to first study dose; palliative steroids are allowed, but must be at a dose equivalent of =\< 20 mg prednisone daily for at least 1 week prior to treatment initiation * Patients capable of reproduction and male patients who have partners capable of reproduction must agree to use an effective contraceptive method during the course of the study and for 2 months following the completion of their last treatment; females of childbearing potential must have a negative beta-human chorionic gonadotropin (B-hCG) pregnancy test result within 3 days of first study dose; female patients who are surgically sterilized or who are \> 45 years old and have not experienced menses for \> 2 years may have the β-hCG pregnancy test waived * Patients must be able to swallow whole capsules * Inclusion of women and minorities: patients of both genders and all racial/ethnic groups are eligible for the study if they meet eligibility criteria outlined; to date, there is no information that suggests that differences in drug metabolism or disease response would be expected in one group compared to another; the small number of patients in a phase II trial precludes any analysis of data to compare patient subgroups based on gender or race/ethnicity Exclusion Criteria: * Previous treatment with a CD19 antibody; prior lenalidomide is acceptable for patients on cohort 2 * Patients who have received alemtuzumab within the previous 6 months * Patients with active Richter's transformation * Patients with active graft versus host disease or active autoimmune condition related to CLL * Female subject that is pregnant or breastfeeding; women of childbearing potential and men must agree to use adequate contraception prior to study entry, duration of study participation, and 30 days following study completion; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately; confirmation that the subject is not pregnant must be established by a negative serum B-human chorionic gonadotropin (B-hCG) pregnancy test result obtained during screening; pregnancy testing is not required for post-menopausal or surgically sterilized women * Patients with congestive heart failure in whom pre-treatment hydration would be prohibitive; New York Heart Association (NYHA) class III/IV congestive heart failure (CHF) is excluded * Patients who have had treatment for CLL within 4 weeks, although palliative steroids are acceptable at doses =\< 20 mg prednisone daily * Failure to recover from toxicity of previous radiotherapy or chemotherapy to grade 1 * Patients with active infections requiring IV antibiotic/antiviral therapy are not eligible for entry onto the study until resolution of the infection; patients on prophylactic antibiotics or antivirals are acceptable * Patients with a known hypersensitivity to lenalidomide * Patients who are known to be human immunodeficiency virus (HIV) or hepatitis C positive * Patients who are known to have hepatitis B infection or who are hepatitis B core antibody or surface antigen positive; patients receiving prophylactic intravenous immunoglobulin (IVIG) may have false positive hepatitis serologies; patients who are on IVIG who have positive hepatitis serologies must have a negative hepatitis B deoxyribonucleic acid (DNA) to be eligible * Patients with a history of prior malignancy other than CLL that requires active systemic therapy that will interfere with interpretation of efficacy or toxicity, or limit survival to 2 years; patients with basal or squamous skin carcinoma, cervical carcinoma in situ on biopsy, localized breast cancer requiring hormonal therapy or localized prostate cancer (Gleason score \< 5) are eligible * Patients with substance abuse or other medical or psychiatric conditions that, in the opinion of the investigator, would confound study interpretation or affect the patient's ability to tolerate or complete the study