Lucifer then continued to speak with a heavier tone, "I want your loyalty."
Lucifer wanted to make sure that Rachel wouldn't be able to betray him or something like that.
Of course, there was no way to know that unless Rachel was an old subordinate from when Lucifer was still active in wars, but it was pretty obvious that Rachel was a young demon.
However, even if there was no way to know for sure, Lucifer...still wanted to make sure.
Although it was complicated and all, it was actually not since it was Lucifer who would be doing it.
Anyways, when Lucifer said that he wanted Rachel's loyalty, Rachel quickly spoke, "What do I have to do to prove my loyalty..."
Rachel knew that just saying that she would be loyal to Lucifer from now on doesn't really mean anything. After all, one can say glorious words when in front of another and say all the cruelest words behind his back.