"So when God desired to show more convincingly to the heirs of the promise the unchangeable character of his purpose, he guaranteed it with an oath, so that by two unchangeable things, in which it is impossible for God to lie, we who have fled for refuge might have strong encouragement to hold fast to the hope set before us." (Heb 6:17-18)
Often we speak of man's inability (at least those of us from Reformation traditions), but seldom do we speak of God's inability. The idea is somewhat shocking because we often think of God's attributes, such as omnipotence, as excluding any idea of inability. Yet the word "impossible" in Heb 6:18 conveys a sense of impossibility and inability. God cannot lie.
God's will is bound to His very nature and character. I am not sophisticated enough, philosophically, to understand exactly how the will and nature relate (or, for all I know, if they are even distinct at all), but in this regard it seems suitable to say that God's will in unable because it is bound to His perfectly holy nature. The thing that is somewhat ironic is that this kind of inability is good. We normally think of inability as a negative quality. We think of it as something which makes its object less than perfect. However, in God's case this inability flows from His perfection without any contradiction whatsoever. His inability is an inability to be less than holy, less than Himself. He is unable to cease being Himself.
With the fallen race of Adam, our wills are bound to a sinful, corrupted nature, which is in love with sin and is unable to do that which is pleasing to God or submit to Him from the heart. Yet God has perfect inability. It is the kind of inability we long for, and the kind of inability we fallen, God-regenerated, believing sinners will experience in glory. That is only part of our blessed hope, the full essence of which being Christ Himself in our midst for our everlasting enjoyment and worship, yet for now we groan inwardly, as Paul noted, awaiting the redemption of our bodies.
With God's inability there is wondrous assurance. God cannot lie. He would more surely cease being God than ever break one of His promises. His inability translates into His steadfast, merciful, joyous, abiding, unwavering will to fulfill all of His gracious promises to us undeserving sinners. Let every doubt which we conceive of in our hearts, let every whisper of the enemy come crashing into this stone wall and fall into the abyss. He is an everlasting Rock.
"Trust in the LORD forever, for the LORD GOD is an everlasting rock." (Isa 26:4)