This study is an open-label, multicenter, phase 1, dose escalation study of TAK-659 in adult participants with advanced solid tumor and lymphoma malignancies. This study will be the first to administer TAK-659 to humans. The participants population during dose escalation (Part A) will consist of adults previously diagnosed with any form of a solid tumor or lymphoma for which standard, curative, or life-prolonging treatment does not exist or is no longer effective. This first-in-human (FIH) study will include 5 dose expansion cohorts in refractory and/or relapsed Chronic Lymphocytic Leukemia (CLL), Diffuse Large B Cell Lymphoma (DLBCL), indolent Non Hodgkin Lymphoma (iNHL), Mantle Cell Lymphoma (MCL), Post Transplant Lymphoproliferative Disorder (PTLD) (Part B) following completion of dose escalation (Part A).