The old, unregenerate self, originating in Adam (see notes on Rom. 5:12-14; 6:6; Eph. 4:22).
“Seeing” means “since.” The “old man”, is all that a person was prior to salvation: his worldly thinking and sinful acts. Since all this was renounced at conversion, one should “lie not.” Falsehood ill becomes the person claiming to be a disciple of Him who said, “I am the … truth.”
We can see from the following Scripture, where lies come from.
John 8:44 “Ye are of [your] father the devil, and the lusts of your father ye will do. He was a murderer from the beginning, and abode not in the truth, because there is no truth in him. When he speaketh a lie, he speaketh of his own: for he is a liar, and the father of it.”
Look with me at the seriousness of lying in the next verse.
Revelation 22:15 “For without [are] dogs, and sorcerers, and whoremongers, and murderers, and idolaters, and whosoever loveth and maketh a lie.”