Augustine of Hippo

"For truth is not in their mouth" (ver. 9). To whose judgment of course then there is no trusting, and therefore must we fly within to conscience, and the sight of God. "Their heart is vain." How then can truth be in their mouth, whose heart is deceived by sin, and the punishment of sin? Whence men are called back by that voice, "Wherefore do ye love vanity, and seek a lie?" "Their throat is an open sepulchre." It may be referred to signify gluttony, for the sake of which men very often lie by flattery. …

Exposition on Psalm 5 ↗

Jerome

For there is no truth in their mouth. The heretics are described; the man of blood and deceit is described, whom the Lord shall abhor. There is no truth in their mouth: they do not have Christ the truth in their mouth, because neither do they have Him in their heart. Their heart is vain. It reads better in the Hebrew: 'Their heart is ἐπίβουλον (treacherous).' For the heart of the heretics truly lies in wait for all whom it deceives. Their throat is an open sepulchre. …

Homily 2, on Psalm 5 ↗

Thomas Aquinas

Then when he adds "For," he assigns the reason for the petition and describes the enemies and the imminent danger. First, from the lack of good. Second, from the abundance of evil, at "For their heart," etc. The deficiency is that if they kept peace, he could be at peace with them and proceed safely. But "there is no truth in their mouth," because they have one thing in their mouth and another in their heart: Hos. 4: "There is no truth." And therefore I cannot proceed safely. Likewise, from the abundance of evil. …

Exposition on the Psalms of David ↗