It's hard to say, Mom, but since homework seems to be the only area that involves lying....I'd suggest rewarding him on the days he is truthful about his homework. Instead of scolding him or making an issue of him lying on the other days. Just something simple like thirty minutes extra at bedtime or offer him something bigger if he is honest each evening for a week....a trip for ice cream or letting him pick a movie to rent, etc. Nothing really expensive. Whatever he shows an interest in. *Sometimes* focussing on the positive instead of the negative is enough of a switch to make a difference.
I know there are so many times by the end of the day that I just don't want to have to do anything else. And, maybe it's just a bad habit. But, look to see what it is that he's in such a hurry to do each evening. If it's play outside...then let him have half an hour of playtime for a break. Or, if it's the computer....give him extra time on it if he's truthful and does his homework first and without a fuss. Same way with television.
I am wondering if he's a third grader?? Seems to me that with my own children and now my grandchildren....that third grade was a difficult year. Not just accademically...but in emotional development, too. That was the year of more arguments, and such. Things settled down after that year. But, you can't let him get away with it either.
Good luck and God Bless.