On second thought, Lady would probably need to consider telling Fallon after all.
Even though she's the creator of this world, she's no longer sure how exactly the story will go from here on out. His existence alone might make a huge difference. He should've been dead by this point, but instead, he's right before her now – alive and breathing and pressuring her to confess.
And with him interrogating her in regards to something he should have not been aware of, she finds herself confronting an important issue.
The main reason why she didn't let anyone know that she's aware of the true purpose of the whole attempted assassination was because she didn't want to reveal the truth - one that could lead them to find out about who she really was. She could make up a lie, but if she was just going to do that, she thought it would be better to keep it a secret instead.