This is the technical difference between lay and lie:
You lay an object onto a surface.
Could you lay those mats on the floor, please?
She laid the books on the table.
The workers are laying the carpet in the new building.
Again, you lay an object onto a surface. But a person/thing lies (itself) on the surface:
There was a package lying on my doorstep.
The clothes are lying all over the floor.
For a person, to lie + a preposition of place means to put yourself horizontally on a surface:
I'm feeling sick. I need to lie down.
She's lying on a towel on the beach.
Now... to complicate matters - the past tense of lie is lay!
Present Continuous Past Past Participle
LAY LAYING LAID LAID
LIE LYING LAY LAIN
Also, native English speakers often say "I need to lay down" and "She's laying on a towel on the beach." - even though it's incorrect!
You lay an object on a surface.
We laid the flowers on the grave.
You lie (yourself) on a surface.
He's just lying there on the couch watching TV.
An object lies on a surface.
There was an abandoned bicycle lying on the sidewalk.
This lesson refers to the meaning of "lie" as an object lying on a surface. There's another meaning for "lie": to say something that isn't true. In this case, the past and past participle would be lied and lied:
The little boy ate the cookies, then lied and said his sister had eaten them.