It looks like people are addressing the executive function piece, but not the lying. As it appears that it's a coping strategy of not being able to handle the organizational demands, of course addressing the root of the problem makes sense.
We've addressed these twin issues of weak executive function and lying about it afterwards by giving our kids a formula for messing up with the logic that lying (or neglecting to mention) is not helping the situation long term, but instead a function of the short-term anxiety and sense of failure. So in our house, we've structured how to make a mistake. We've found that it helps address the anxiety around the problem so that they can actually learn. It's the 4 F's. Mess up, Fess up, Fix it, and Forget it/Move on.
Mess up, e.g. forget to hand in homework
Fess up (and apologize): admit to your mistake and be able to name it. "Mrs Teacher, I'm sorry I forgot to hand in my homework. I hope you will accept it now."
Fix it: "I'm going to try carrying a homework folder with me to every class from here on," or, "Can you help me remember to get the homework out of my folder until it's a habit?"
Forget it or move on. It's in the past. You've got your fixes in place now, no need to dwell on it.
