lay down
phr. v.. B1 Intermediate Oxford
phr. v.. to put something in a place, or to establish a rule or condition.
phr. v.. to place something in a specific location; to establish a rule, condition, or principle. The verb 'lay' is transitive, requiring a direct object.
He lay down the book on the table.
The teacher laid down the rules for the exam.
The company laid down strict guidelines for employee conduct.
From Middle English leyen doun, leien doun (“to lay down”), equivalent to lay + down.
Usage
takes a direct object — the thing being placed or the rule being established.
Teaching tip
contrast with 'put down' (more about physical placement) and 'set down' (formal equivalent for establishing rules).