EXACTLY. That is why it is impossible for God to lie. NOT because God is less powerful than man (ability) but because God is righteous and this is His nature.God is the source of the moral law, not its subject. God cannot lie, because He is the Truth. If God could, in some future moment* change His mind, if it were possible for Him to deny Himself, to be corrupted, then you have no real basis for your faith.
Accept it as it is written, because it is the truth. God cannot deny Himself. He is immutable. Not because He promised not to change His mind, but because He cannot.
*God is eternal, and in Heaven there is no past or future as we think of them. It is past, present, and future simultaneously existing as now.
We cannot measure the standard by the standard....that does not make sense. The standard IS the standard. And God is the Standard of righteousness. It is impossible for God to lie because God is righteous, holy, pure, immutable....because God is God.