Can God lie? This is one of those types of questions which you might find yourself trying to answer were you to ever engage in a lengthy apologetic conversation with a skeptic. I have to admit, it's not a question that I have ever given much thought, but just the same--the Bible provides us with a definitive answer, even if it is not an elaborate one. Paul, a bond-servant of God and an apostle of Jesus Christ, for the faith of those chosen of God and the knowledge of the truth which is according to godliness, in the hope of eternal life, which God, who cannot lie, promised long ages ago, but at the proper time manifested, even His word, in the proclamation with which I was entrusted according to the commandment of God our Savior, To Titus, my true child in a common faith: Grace and peace from God the Father and Christ Jesus our Savior. (Titus 1:1-4 NASB, emphasis added)
Paul, in this brief introductory portion of his letter to Titus, states very plainly that God cannot lie, and as I mentioned before its not an elaborate answer. Neither is it a question that needs an elaborate answer, but I do feel like I might have some small understanding of why God cannot lie. Of course, to engage in this line of thought is to at the same time answer the question as to why God would ever need to lie--the answers to both are tied quite neatly together.
God cannot lie, nor does He need to, because any way that He chooses to communicate to His people is true. If He says it, it is. This is why when Moses asks God in the Book of Exodus, "who should I tell them sent me?" God simply refers to Himself as "I AM". Moses, and us as well, are sorely incapable of really grasping what or who exactly God might be, at least in an easily definable way. So God makes it easy for Moses.
He exists. He is. He is the God that changes not. The Immortal I AM. The same yesterday, today, and forever. He is our Alpha and Omega, that is our entire existence is contained within His sovereign infinitude.
God cannot lie because there can be no truth apart from Him.