"Lay down" might be fine, it just depends on the context, and the verb you're intending to use!
The verbs are to lay (put something down), and to lie (become horizontal) but confusingly, the simple past tense of to lie is lay. To make it even worse, the past tense of to lie (tell fibs) is lied.
Present tense:
I lay the coat on the bed. (I am laying...)
I lie on the bed. (I am lying...)
I lie about my past.
Simple past tense:
I laid the coat on the bed.
I lay on the bed.
I lied about my past.
Perfect tense:
I have laid the coat on the bed.
I have lain on the bed.
I have lied about my past.
So it would be "lay down your burdens, then have a lie down".