This is an open-label, dose-escalation Phase 1/2 study to assess the safety of ASTX660, determine the maximum tolerated dose (MTD), recommended Phase 2 dose (RP2D), and recommended dosing regimen, and to obtain preliminary efficacy, pharmacokinetic (PK), and target engagement data, in subjects with advanced solid tumors or lymphoma for whom standard life-prolonging measures are not available.