“How can I be holy when I have sin and am aware of it?”

Let Christians strive to learn completely and perfectly this doctrine of Christian righteousness … they will find that this is the situation, that Christian righteousness consists in two things: first, in faith, which attributes glory to God; secondly, in God’s imputation. For because faith is weak, as I have said, therefore God’s imputation (God’s act of giving the believer the credit for having righteousness) has to be added. That is, God does not want to impute the remnant of sin and does not want to punish it or damn us for it. But He wants to cover it and to forgive it, as though it were nothing, not for our sakes or for the sake of our worthiness or works but for the sake of Christ Himself, in whom we believe.
Thus a Christian man is righteous and a sinner at the same time, holy and profane, an enemy of God and a child of God. None of the sophists will admit this paradox, because they do not understand the true meaning of justification. This was why they forced men to go on doing good works until they would not feel any sin at all. By this means they drove to the point of insanity many men who tried with all their might to become completely righteous in a formal sense but could not accomplish it.
We, on the other hand, teach and comfort an afflicted sinner this way:
“Brother, it is impossible for you to become so righteous in this life that your body is as clear and spotless as the sun. You still have spots and wrinkles (Eph. 5:27), and yet you are holy.”
But you say: “How can I be holy when I have sin and am aware of it?”
“That you feel and acknowledge sin—this is good. Thank God, and do not despair. It is one step toward health when a sick man admits and confesses his disease.”
“But how will I be liberated from sin?”
“Run to Christ, the Physician, who heals the contrite of heart and saves sinners. Believe in Him. If you believe, you are righteous, because you attribute to God the glory of being almighty, merciful, truthful, etc. You justify and praise God. In short, you attribute divinity and everything to Him. And the sin that still remains in you is not imputed (credited against you) but is forgiven for the sake of Christ, in whom you believe and who is perfectly righteous in a formal sense. His righteousness is yours; your sin is His.”
As I have said, therefore, any Christian … first, he offers and slaughters his reason and the mind of the flesh, and, secondly, he attributes to God the glory of being righteous, truthful, patient, kind, and merciful. This is the continuous evening and morning sacrifice in the New Testament. The evening sacrifice is to kill the reason, and the morning sacrifice is to glorify God. Thus a Christian is involved, daily and perpetually, in this double sacrifice and in its practice. No one can adequately proclaim the value and the dignity of Christian sacrifice.
Therefore this is a marvelous definition of Christian righteousness: it is a divine imputation or reckoning as righteousness or to righteousness, for the sake of our faith in Christ or for the sake of Christ.  Therefore this inestimable gift excels all reason, that without any works God reckons and acknowledges as righteous the man who takes hold by faith of His Son, who was sent into the world, who was born, who suffered, and who was crucified for us.

Martin Luther.
Luther’s Works, Vol. 26 : Lectures on Galatians  26:232 Saint Louis