Well it would hardly make sense to split one word up in two lines, now would it? "I long to be like you, sis, lie cold in the ground like you, ter" ? Yeah, that's amazingly brilliant English.
By saying "lie cold in the ground like you did", not only does it make sense, to me, Amy is saying that her sister isn't in the ground anymore - she's moved on to the next world, or Heaven or whatever you want to call it. And Amy wants to be with her.
"like you did" makes more sense than "you ter" and I think those of us who can hear it are probably right.
