Is “Now I lay me down to sleep” grammatical?

Solution 1:

Technically this is grammatically correct, however it is not common for someone to use the first person for both the subject and the direct object of a sentence, as it comes across as somewhat redundant.

"Now I lay down to sleep" has the same meaning and is a more conventional way of saying this. Although I'm sure the choice to use "Now I lay me down to sleep" was done for poetic reasons and there's nothing wrong with that.