Delilah's limit breaks do not work like canon Aerith's.
( My reasonings, let me show you them. )

"Delilah" is a bit of a work in progress at the moment; I've had the rough idea bouncing in my head for a while, but the finer points are still being hammered out.  Toss in that she's a deceiver, liar, and certified headcase, and what she tells people might very well clash with what she's said before.  Here, at least, are the points that are clear:

( Known Relations (or lack of) )