I've read that lying is actually a specific and importan developmental stage. DD now has some model of what is going on in your head. She's moved beyond dealing with the apparently random acts of adults, and is now trying to manipulate them.
As such, to them it's not a "moral" thing at all.
also they will observe that adults are not 100% honest. When you say "we'll play with that later", does it always happen ? Small things to you perhaps.
Obviously I have no idea about your discipline regime, but we've been firm on politeness, and they just don't get things without "please, thankyou" etc. That's a a long slog, and never 100% of course.
We've also gone in for extending references over time.
If you promise a kid X, then not just do it a day or two later, but also say "we promised you X on Tueday, and so here it is".
Kids notion of time is different to ours, and "truth" is a sort of function of when things happen. Some cultures, especially oriental ones have more a "now" view of things, and that's like a child's view. Things other than "now" aren't so real, and thus they are what you think they are.
Thus although it's possible that DD was lying to get out of trouble, her model may well have been that if she believed what she said about the past, then it was all right. Thus she would have been confused, not educated if you were to give her a bad time over it.