Antonyms for the phrase "lays at one's door" include "exonerated," "vindicated," and "acquitted." These words suggest that someone has been cleared of blame or responsibility for a particular problem or situation. Other antonyms might include "shared," "diffused," or "dispersed," which imply that responsibility for an issue is spread out among multiple parties rather than exclusively shouldered by one individual. These antonyms can be useful when discussing the allocation of blame or responsibility in a given situation, and can help to clarify whether fault lies with one person, a group, or no one at all.
