Bcl-2 Inhibitor GDC-0199 in Combination With Obinutuzumab and Ibrutinib in Treating Patients With Relapsed, Refractory, or Previously Untreated Chronic Lymphocytic Leukemia

Inclusion Criteria: * Diagnosis of CLL meeting criteria established in the World Health Organization (WHO) classification of hematologic disorders * Eastern Cooperative Oncology Group (ECOG) performance status =\< 1 * Relapsed or refractory CLL patients must meet the following requirements: * Received at least 1 prior therapy * Require treatment in the opinion of the investigator * Relapsed patients must have developed progressive disease following a response to a prior therapy * Refractory patients must have failed to respond or relapsed within 6 months to the last prior therapy * Treatment-naïve CLL patients must meet the following requirements (Phase II only): * Symptomatic disease as defined by International Workshop on Chronic Lymphocytic Leukemia (IWCLL) 2008 criteria * Received no prior chemotherapy, immunotherapy, or targeted therapy for the treatment of CLL with the exceptions of palliative loco-regional radiotherapy and corticosteroids for symptom control * Hemoglobin \>= 8 g/dL * Absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelets \>= 40,000/mm\^3 * Prothrombin time (PT)/partial thromboplastin time (PTT) =\< 1.5 x upper limit of normal (ULN) * Total bilirubin =\< 1.5 x ULN (excepting Gilbert's syndrome) * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) =\< 2.5 × ULN * Serum creatinine \< 2.0 mg/dL or creatinine clearance (Cockcroft) \>= 50 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Fem…