First of all, we cannot separate the Lordship of Christ from His being being the Savior for the one who died on the cross was the LORD Jesus Christ.
When we receive Him as Savior, we receive the entirety of His person, both His being Lord and His being the Savior. Every saved sinner will manifest the Lordship of Christ in his life somewhere, sometime and somehow, as God progressively sanctifies him.
The Christian progressively bowing and submitting to the Lordship of Christ is the field of sanctification.
The message that must be accepted and believed in order to be justified is the message that Paul preached to the Corinthians when he came and preached in Corinth:
1Co 15:1 Moreover, brethren, I declare to you the gospel which I preached to you, which also you received and in which you stand,
2 by which also you are saved, if you hold fast that word which I preached to you--unless you believed in vain.
1Co 15:3 For I delivered to you first of all that which I also received: that Christ died for our sins according to the Scriptures,
4 and that He was buried, and that He rose again the third day according to the Scriptures,
In order to be saved from the penalty of sin, Paul did not require the Corinthians to submit to the Lordship of Christ. No, he simply preached to them the good news that Christ died for our sins and rose from the dead.
However, when they did believe in the message, Paul's emphasis turned to encouraging the Christians to submit to the Lordship of Christ.
It is at the moment of receiving the word of salvation, the Gospel, that we become followers of the Lord. A saved sinner is a disciple. He has a new nature. He has the indwelling Holy Spirit. He has the mind of Christ.
1Th 1:6 And you became followers of us and of the Lord, having received the word...