They are three different verbs involved here:
Lie - not to tell the truth
(Past simple/past participle: lied/lied )
Lie - an intransitive verb, meaning to stretch out your own body horizontally
(Past simple/past participle: lay/lain)
Lay - a transitive verb, meaning to put down carefully
(Past simple/past participle: laid/laid)
These verbs can be confusing. In certain accents, it can be hard to tell whether person is saying 'lie' or 'lay'. The other problem is that many native speaker use the second two verbs incorrectly. But even with these two levels of confusion, you should always be able to tell from the context what the speaker actually means.