Now I lay me down to sleep.....

Grammar 101: to lie is an intransitive verb - i.e. it doesn't take a direct object - "lay" is the past of this verb.
To lay is a transitive verb which means it requires a direct object: its past and past participle are both "laid".
What brought this on, do you ask? The sight of a printed notice which failed to differentiate between the two: unfortunately I didn't have a black marker pen to hand, so I took a photo instead.

Exhibit A

and Exhibit B: what is actually being forbidden, if you take the sign literally.

 

 Added Sept. 2020

Reassure me, surely the irregular past form of "to lie" hasn't been changed and I didn't get the memo?

This caption accompanied a photo taken at the funeral of H.W. Bush on the BBC website.

"In the past few days, however, old wounds seem to have been mended. Mr Trump welcomed the family to the Blair House, across the street from the White House, and paid his respects as the elder Bush laid in state at the US Capitol."

https://www.bbc.com/news/world-us-canada-46449637