If she thinks it's likely he'll desummon her (whether on purpose or by accident) and wants to exist more than she wants him to know the truth, then she probably shouldn't.
If she wants to maintain any sort of trust between him and her that isn't a ticking time bomb in disguise, that ship's probably already sailed, but I'd imagine trying to defuse said bomb now (or near to now) rather than having it go off at the worst possible moment would be best.
I haven't posted yet (because fatigue not make brain work so good), but I suppose the main thing Lucifer's thinking is why would she let anyone, much less the absolute worst person in the group (as far as keeping secrets is concerned) in on such sensitive information.