Why does she put "me" after "lay"? Is it necessary?
"Lay me down" is actually an idiom. In this context, it means 'I won't give up". So, she is saying that she is not willing to give up and die, it's a little bit dramatic but, simply means she's going to keep fighting for what she believes in. The idiom can also have the meaning of "to rest". So it could also be viewed that she's saying she won't rest until she achieves what she's fighting for. The phrase "lay me down" is quite old-fashioned and isn't something you'll hear often outside of shows and movies or in songs for poetic purposes.