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The word lay is confused in more than one way. Please note that there are multiple groups on this page.

lay to set down or place something
lie to recline; to tell a falsehood

Examples  

Lay your weapons on the table.
I like to lie in the sun by the lake.
I don't lie, said George Washington.
lay to place horizontally (active past tense of lie)
laid put down (past tense and past participle of lay)
lain to be horizontal (past participle and passive past tense of lie)
lied told a falsehood (past tense and past participle of lie)

Examples  

I lay in the sun all day yesterday.
George Washington never lied.
She laid her cards on the table.
She was laid to rest.
She had lain in the sun all afternoon.