No - Dr. Martin Luther did not write this carol.    However, the words and he concepts are really quite simple: there is Jesus at His birth, sleeping in His manger bed in Luke 2:7 - “And she gave birth to her firstborn son and wrapped him in swaddling cloths and laid him in a manger, because there was no place for them in the inn.”    The author undoubtedly wanted little children to know that the Little Lord Jesus, now in heaven, is looking down on them and is very near them when they, too, are lying in bed sleeping.  Matthew 28:20 tells us this very thing; “and behold, I am with you always, to the end of the age."   We know that Jesus will stay close to me all of my life, and when I die, Jesus will take me and all His dear children in His tender care to be with Him in heaven.  
What a picture of Jesus we have.   Despite distractions, Jesus is lying in His bed sleeping.  This little one will, in 33 short years, offer His life on a cross for our forgiveness.  But for now, just sing of the sweetness and joy of the Child in the Manger - He is so small - and yet - He is the Lord of all.

Away in a manger, no crib for a bed,
The little Lord Jesus laid down His sweet head.
The stars in the bright sky looked down where He lay,
The little Lord Jesus asleep on the hay.

LSB 364 / 365