Is it possible that the reason he is lying is because he sees it as the only way to have any control over how overwhelmed he is?
We have an accomodation that allows us to diminish work load on nights when he's overwhelmed, and it completely changed his attitude. He needs down time - his poor brain is exhausted from keeping up at school and then being taxed with all the work that completely exhausts him in ways it doesn't for others.
Unless you see the lying in other parts of his life, I'd see this as a cry for help and go back to the school and ask for reduced work load on nights that there is an inordinate amount of written work assigned or on nights when you can see your kiddo is more exhausted than usual.
