Go to sleep and Lay down

Go to sleep verb - Prepare for sleep.

Lay down and go to sleep are semantically related In some cases you can replace term "Lay down" with "Go to sleep", this terms are similar.

Lay down verb - To put into effect through legislative or authoritative action.

Go to sleep and lay down are semantically related in go to bed topic. Sometimes you can use "Go to sleep" instead a verb "Lay down".