The phrase "lays down law" typically refers to someone asserting their authority or making rules that others must follow. Antonyms for this phrase could include "negotiates," "compromises," or "collaborates." These words suggest a more collaborative, cooperative approach to problem-solving and decision-making, rather than a top-down, authoritarian approach. Other antonyms could include "listens," "respects," or "embraces diversity." Using these approaches can lead to more inclusive, equitable outcomes that prioritize the needs and perspectives of everyone involved, rather than just those with the most power.