Restitution for older kids-like 6-is GREAT because they feel rewarded by paying for what they did, as well as having a tangible physical result and (unpleasant) experience to their wrong choice, and a way to "make good on it". My oldest is 5 and hasn't been caught lying since she fibbed at 3, but we have lots of cousins in this age range who rarely act up, lie, and all that, but when they do, they are given hard chores to do.
They HATE the chores, but they always feel a sense of satisfaction when they're done. They also get thanks and credit for doing the job. However, the next time they get a warning along with a , "Hey, I wouldn't do that, because the garage shelves need to be cleaned off and washed, or the firewood needs to be moved up to the house" they LISTEN. It's not as pointless and unrewarding as sending a moping kid to brood in their room without a video game or something, which tends to make behaviors worse over time when people allow the angry kid to go self implode in their room over how they've been slighted and denied something.
They will sometimes ALSO remove a privilege until it can be earned back if the offense warrants compounded discipline, but toys and things of that nature area luxury to begin with, and removing them is sort of a lack of consequence since there is still nothing serious for the child to experience for their actions. Also, these kids have lots of chores to begin with, so having extra ones is a drag. It's doesn't put a sour face on chores in general.
I would give your son lots of praise for coming forward with the truth and give him a way to "pay it off" and illustrate that his consequences for the lie would have been a lot worse. Emphasize your pride in the truth. I would say to skip the consequence too, but kids really do like earning back their respect. Either one would be good in this case. You know your son.
Just a thought! And congrats on having a child with a great conscience! The discpline you've been using so far has accomplished that :)