Every child who is diagnosed with ADHD or any psychiatric disorder and taking prescribed medication needs to be seeing a mental health therapist. This is where you need to begin.
I agree with Mark. All studies have shown that the most effective treatment for ADHD is BOTH behavioral therapy and medication. And recent studies have shown that it is possible to reduce the medication due to the therapy.
And in regards to his lying. "kids with ADHD are especially prone to stretching the truth." "First, realize that the impulse to tell fibs does not make your youngster a bad person, nor is it evidence of a character flaw. It’s just a byproduct of ADHD — almost a symptom." The rest of the article gives some good advice on things that you can do. http://www.additudemag.com/adhd/article/2008.html
And part of the problem is that your son is only 10. At that age he still does not have a lot of control over himself. And with ADHD, he will certainly do and say things without thinking. I wonder if the lying is worse as his meds are wearing off and he has less control?
This is a good link to the importance of behavioral therapy. You might want to check it out and then send it to his dad - http://www.goodtherapy.org/blog/beyond-the-medication-behavioral-treatment-for-adhd-0507145
Hope this helps. Best wishes.