The phrase "lay at door" means to place the blame or responsibility on someone or something. Antonyms for this expression could be words like absolve, exculpate, or exonerate that mean to clear or declare innocent. Other antonyms could be words like vindicate or acquit, which indicate a verdict of not guilty or a finding of innocence. Additionally, terms like exonerate, defend, and protect can all imply a sense of shielding or safeguarding from any sort of blame, punishment, or accusation that might come one's way. Ultimately, the antonyms for "lay at door" are words that point to innocence, exoneration, and vindication.