cHL COHORT ONLY: history of allogeneic transplant Previous allogeneic bone marrow transplant Patients with previous allogeneic bone marrow transplant Prior allogeneic transplant Previous allogeneic transplant Subject with a history of organ transplant or allogeneic bone marrow transplant; Prior allogeneic transplant Has received an allogeneic bone marrow or allogeneic stem cell transplant. History of an allogeneic bone marrow transplant. Prior allogeneic bone marrow transplant. Participants who have received a previous allogeneic bone marrow transplant Participant has had a prior allogeneic transplant. Subjects with clinically significant cardiovascular disease, history of organ transplant or allogeneic bone marrow transplant, active known or history of autoimmune disease that might recur or major surgery within 28 days prior to the first dose or still recovering from prior surgery. Participants who are within 6 months of an allogeneic bone marrow transplant the subject has recovered from transplant-associated toxicities prior to the first dose of GSK525762, and For subjects with a prior history of allogeneic transplant, Clinically significant pulmonary dysfunction, active infection, prior allogeneic bone marrow transplant, active autoimmune disease Prior allogeneic transplant if performed < 6 months prior to first dose of AMV564, if patient has active GVHD, or if patient has not been off immunosuppressive Previous allogeneic transplant Prior allogeneic bone marrow transplant within 12 months of screening date Prior allogeneic transplant, within the last 5 years We will exclude patients who are eligible for an allogeneic bone marrow transplant at the time of study enrollment; if an enrolled patient subsequently becomes eligible for transplant, they will not be prevented from proceeding to the appropriate clinical treatment indicated FOR ALL PHASES (Ib AND II): History of having received an allogeneic bone marrow or organ transplant Previous allogeneic bone marrow transplant Prior allogeneic bone marrow transplant Prior allogeneic transplant Prior allogeneic transplant Willingness to have an allogeneic transplant Have undergone a prior allogeneic bone marrow transplant (BMT) PART 1: History of prior allogeneic transplant History of an allogeneic solid organ transplant or bone marrow transplant, or current active immunosuppressive therapy such as cyclosporine, tacrolimus, etc. Allogeneic transplant with a human leukocyte antigen (HLA)-identical sibling will be recommended for patients < 55 years; if the patient refuses allogeneic transplant, they may still be eligible for this protocol Prior allogeneic transplant Patients with secondary AML, and patients with a prior autologous and allogeneic bone marrow transplant are eligible Subject has a history of organ transplant or allogeneic bone marrow transplant; Receipt of an allogeneic bone marrow or allogeneic stem cell transplant Patients who received an allogeneic bone marrow or allogeneic peripheral blood stem cell transplant less than 12 months prior to initiation of study Has a transplanted organ or has undergone allogeneic bone marrow transplant Patients eligible, at the time of starting treatment, for curative therapeutic approaches (such as allogeneic transplant) are not eligible for the trial; however, patients who achieve CR or partial response (PR) as a result of therapy on this trial may proceed to allogeneic transplant Prior allogeneic transplant Prior allogeneic bone marrow transplant Patients with an organ transplant, including those that have received an allogeneic bone marrow transplant. History of having received an allogeneic bone marrow or organ transplant History of an allogeneic solid organ transplant or bone marrow transplant, or current active immunosuppressive therapy such as cyclosporine, tacrolimus, etc. Previous allogeneic bone marrow transplant. Prior allogeneic transplant of any kind Eligible for allogeneic transplant in the treating physicians’ judgment and by institutional standards Previously received an allogeneic transplant Autologous or allogeneic bone marrow transplant as second-line therapy. Prior allogeneic transplant Prior allogeneic transplant > 60 days after reduced intensity conditioning (RIC) allogeneic transplant for lymphoma Prior allogeneic transplant Has received an allogeneic bone marrow or allogeneic stem cell transplant. Eligible for allogeneic bone marrow transplant. Receipt of an allogeneic transplant. No more than 4 prior lines of systemic anti-cancer therapy and no prior bone marrow transplant or stem cell transplant within 12 months of dosing, and no prior allogeneic transplant. Subjects who received an allogeneic bone marrow or allogeneic peripheral blood stem cell transplant Previously received an allogeneic transplant. Any prior allogeneic transplant. Allogeneic transplant recipients undergoing ablative transplants will also be eligible to participate; those receiving nonablative regimens (a small proportion of allogeneic transplant recipients at UWCCC) will be excluded Patients who have failed a prior autologous or allogeneic transplant are eligible; however, at least 6 months must have elapsed between the start of this reduced intensity conditioning regimen and the last transplant if patient had a prior autologous or myeloablative allogeneic bone marrow transplant (BMT) Prior allogeneic transplant Underwent a previous related or unrelated allogeneic transplant Prior allogeneic transplant Prior allogeneic transplant Patients who have received a prior allogeneic transplant will be excluded Subject has had prior allogeneic transplant. Has received an allogeneic transplant in the past; scheduled to receive a second allogeneic transplant Prior allogeneic BMT