The words Lay and Lie are verbs that are often used incorrectly. One of the reasons is that there are two Lay verbs. One is the base form of the verb Lay, and the other is the past tense of the verb Lie.
Lay is a transitive verb meaning 'to put or place.' Someone lays something down.
(Note: Lay is also a widely recognized slang verb or noun involved with sexual intercourse. Examples are 'John wants to lay Mary.' or 'Linda is a good lay.' The lay that is involved with sexual intercourse is not under discussion here.)
Lie is an intransitive verb meaning 'to rest on a more or less horizontal surface.' Someone lies down on a more or less horizontal surface.
(Note: Lie is also both another verb and a noun. The verb Lie can mean to tell other than the truth. The noun Lie is a statement that is other than the truth. The Lie, either verb or noun, that involves other than the truth is not under discussion here.)
Both Lay and Lie are irregular verbs. Of course it adds to the confusion that Lay is not only a present tense of the verb Lay, but also the past tense of the verb Lie.
Present
Lay: 'He lay the woman on the bed.' 'They lay the woman on the bed.'
Lie: 'He watched the woman lie on the bed.' 'They watched the woman lie on the bed.'
Present Participle (continuing action)
Is/Are Laying: 'He is laying the woman on the bed.' 'They are laying the woman on the bed.'
Is Lying: 'He is watching the woman who is lying on the bed.' 'They are watching the women who are lying on the bed.'
Past
Laid (past tense of Lay): 'He laid the woman on the bed.' 'They laid the woman on the bed.'