There is no such thing as a Christian who has not come under the Lordship of Jesus Christ. O ur Lord clearly indicates that they are not. Christian salvation is personal. Christ will reign in a Christian's heart by faith. But the Bible never uses these concepts in Gospel invitations.
Scripture always uses the more direct language of repentance and faith.
Our fundamental problem is not that we are separated from God. We are, as a result of that, alienated sinners, separated from the life and blessing of God. God's wrath is poured out upon His Son, instead of us. That is the substantive heart of the gospel proclamation. It is primarily legal and forensic, not existential.