lie down on
lie down on (someone or something)
To rest or recline on someone's or something on one's back. Why don't you go lie down on the sofa and close your eyes for a little while? Thomas, quit lying down on your baby sister like that! You could hurt her!
lie down on something
to recline on something. Don't lie down on that couch! I will just lie down on my bed for a few minutes.