God doesn't lie because he says so.

[Angrboda]

I've never thought about the fact that if God can't lie then he's not omnipotent. Good point.

It's not that God can't lie, but He doesn't lie.

Theists believe that God is truthful/trustworthy and He won't do something which goes against His own attributes (truthful being one of them). Therefore, He's not going to lie.

That doesn't mean that He "can't" lie.

I hate to say it, but you end up with the same problem only once removed. If it's in his nature that he won't lie, then he cannot lie. Unless God can do what is not in his nature.