Obinutuzumab and ICE Chemotherapy in Refractory/Recurrent CD20+ Mature NHL

Inclusion Criteria: * Patients in first relapse or primary induction failure CD20 positive B-cell leukemia/lymphoma including: * Diffuse Large B-Cell Lymphoma * Burkitt Lymphoma * High Grade B-cell Lymphoma: Not Otherwise Specified (NOS) * Primary mediastinal B-cell lymphoma (PMBL) * CD20+ B-lymphoblastic lymphoma * Follicular lymphoma, Grade III * Karnofsky ≥ 60% for patients \> 16 years of age and * Lansky ≥ 60 for patients ≤ 16 years of age. * Myelosuppressive chemotherapy: Must not have received within 2 weeks of entry onto this study. * Patients may not have received prior therapy with obinutuzumab (GA101) * Radiation Therapy (XRT): Date of receiving prior XRT must be \> 2 weeks for local palliative XRT (small port); \> 6 months must have elapsed if prior craniospinal XRT or if \> 50% radiation of pelvis; \> 6 weeks must have elapsed if other substantial bone marrow radiation. * Steroids: Patients may have received prior steroid treatment, but not started greater than 7 days prior to initiation of protocol therapy. * Adequate organ function. Exclusion Criteria: * Patients with newly diagnosed, previously untreated B-NHL. * Known congenital or acquired immune deficiency. * Prior solid organ transplantation. * Prior allogeneic stem cell transplant within 60 days or active acute Graft-vs-Host-Disease (GVHD) grade 3 or higher. * History of grade 4 anaphylactic reactions to humanized or murine monoclonal antibodies * Uncontrolled hepatitis B and/or C infection