C.M.
I think once kids tell a lie, most kids feel they have to stick with the lie rather than tell the truth. Especially if she is smart.
It sounds like she doesn't like to wash her hands because it interrupts play or whatever she's doing.
I would stop asking her if she washed her hands. You're just making it possible for her to lie. She's smart (and believe it or not, it takes a smart kid to lie) so she's decided it's best to keep playing and lie about washing her hands because there is a chance she will get away with it.
You just have to make it easier for her to comply with the hand washing.
Give her a 5 minute warning that playtime is about to be over. My daughter always worked better with a 5 minute warning rather than just the order to stop playing and to do something else (that she might not really want to do).
You can even set a timer.
At that point, walk her to the bathroom and watch her wash her hands. You'll have to do this for a long time. What you're doing is establishing a habit.
I guarantee, it will become a good habit. You just have to help her make it a habit.
At her age, rather than focusing on the lying, you just need to make it so she doesn't have the opportunity to lie. She's going to lie if she gets the chance. As she gets older, you can introduce a harsher consequence for the lie.