Living in truth means not only being true to oneself. More precisely it means being truthful, being true to God, for he is the source of all truth. We find the truth about God and about all of reality quite directly in Jesus, who is “the way, and the truth, and the life” (Jn 14:6).
Someone who really follows Jesus brings greater and greater truthfulness into his life. He eliminates all lies, falsehood, pretense, and ambiguity from his accomplishments in life and becomes transparent toward the truth. To believe means to become a witness to the truth.