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Do you tell a person to , "Lie down."

Then do you say lay the book on the table?
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Yes.

Lie is intransitive. Lay is transitive - it requires an object.
Comments  
Lay is used when the verb "to lay" is transitive. (Ex. I lay the book down next to the glass.)

Lie is used when the verb "to lay" is intransitive. (Ex. I lie down.)
 BarbaraPA's reply was promoted to an answer.