My question is about the object of saving faith. I know it's Jesus, but a lot of Reformed say that it's accepting Jesus as Lord and Savior, and accepting as Lord means to submit to Jesus’ commandments, the called Lordship salvation. Maybe I am misinterpreting, but it seems to me that it's not so different to say that salvation is faith plus law keeping, or submit to the Law. I read in Clarke’s commentary on Romans (10:9): “That if thou shalt confess, etc. - Acknowledge the Lord Jesus Christ as the only Savior. Believe in thy heart that he who died for thy offenses has been raised for thy justification; and depend solely on him for that justification, and thou shalt be saved." Would the confessional Lutherans agree with that definition of the object of faith? If yes, could you give me some biblical proof? Because indeed in Romans 10 Paul says to confess Jesus as Lord.
The Bible teaches that people enjoy forgiveness of sins and eternal life through faith in Jesus Christ alone (Ephesians 2:8-9). Good works do not play any part in our salvation (Titus 3:4-5).
While it is through faith in Jesus Christ alone that people enjoy salvation, the Bible (especially the book of James) teaches that faith does not exist in a vacuum. Faith is never alone; it displays itself in a life of love. Jesus himself said, “If you love me, keep my commands” (John 14:15).
The Lordship salvation controversy that you referenced describes the approach of some who want to quantify saving faith or add to saving faith as the means to enjoying salvation. The book of Galatians addresses that error.
Since you mentioned “confessional Lutherans,” allow me to pass along a couple of appropriate sections from the Augsburg Confession that address your question.
“Also they [our churches] teach that men cannot be justified before God by their own strength, merits, or works, but are freely justified for Christ’s sake, through faith, when they believe that they are received into favor, and that their sins are forgiven for Christ’s sake, who, by His death, has made satisfaction for our sins. This faith God imputes for righteousness in His sight. Rom. 3 and 4.” [Article IV: Of Justification]
“Also they [our churches] teach that this faith is bound to bring forth good fruits, and that it is necessary to do good works commanded by God, because of God’s will, but that we should not rely on those works to merit justification before God. For remission of sins and justification is apprehended by faith, as also the voice of Christ attests: When ye shall have done all these things, say: We are unprofitable servants. Luke 17, 10. The same is also taught by the Fathers. For Ambrose says: It is ordained of God that he who believes in Christ is saved, freely receiving remission of sins, without works, by faith alone.” [Article VI: Of New Obedience]