This is not a homophone. Homophones sound the same, but lay/lie does not, so it does not fit into the homophone category.
TO RECLINE
present tense: lies/laying down
past tense: lay down
past perfect tense: have lain
TO PUT
present tense: lays [object]/laying [object]
past tense: laid [object]
past perfect tense: have laid [object]
EXAMPLES:
to recline, present tense
The boy is lying down.
to recline, past tense
After school, Mackenzie lay down to take a nap.
to recline, past perfect tense
Jojo has laid down on the couch.
to put, present tense
Suspiciously, the unknown girl lays down a small object behind the bushes.
to put, past tense
The boy laid the obviously stolen pencil on my desk.
to put, past perfect tense
She must have laid the answer sheet on my bed when I was not looking.
Hope this helps; comment if you have any questions!
