1. explain or arrange something carefully and clearly
lay out the options and then make a decision
'Lay out' is a phrasal verb meaning to spread out something or to arrange a number of objects so that they are easily visible. Lay out can also mean to explain something step by step or in a clear way so that it is easy to understand. To lay out something also refers to how something is planned or arranged such as a room, a town or machinery. To lay out for something can also mean to spend money. When a dead body it's prepared so that people can come to view it before it is buried we also use the verb lay out.
To lay down can mean to give up or to surrender, for example, to lay down weapons. To lay down can also refer to an official statement of how something must be done or rules that must be followed. Laid down is also another way of saying lie down which is use more in spoken English. When you lay down the law it means to instruct someone on how to behave or how to act according to your expectations.