Colossians 1:21-22

21 And you, who once were alienated and hostile in mind, doing evil deeds, 22 he has now reconciled in his body of flesh by his death, in order to present you holy and blameless and above reproach before him, 23 if indeed you continue in the faith, stable and steadfast, not shifting from the hope of the gospel that you heard, which has been proclaimed in all creation[a] under heaven, and of which I, Paul, became a minister.

 

Romans 3:24-26

24 and are justified by his grace as a gift, through the redemption that is in Christ Jesus, 25 whom God put forward as a propitiation by his blood, to be received by faith. This was to show God's righteousness, because in his divine forbearance he had passed over former sins. 26 It was to show his righteousness at the present time, so that he might be just and the justifier of the one who has faith in Jesus.

 

2 Corinthians 5:21

21 For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God.

 

John 10:11

11 I am the good shepherd. The good shepherd lays down his life for the sheep. 

 

What did the Lord Jesus accomplish on the cross?

The Lord Jesus on the cross accomplished the entire salvation of God’s chosen people. In John 19:30 we read a recording of Christ’s declaration that it is finished. We learn from Colossians 1:21-22 and Romans 3:24-26 that the declaration of “It is finished” was centered on Christ satisfying and exhausting the infinite wrath of God against sinners whom God had chosen. Christ took their penalty on the cross and died in their place. His righteousness that He actively earned in His life and passively earned in His submission to the Father’s will on the cross is the righteousness of God that is imputed to God’s chosen upon their faith. In essence, Christ Jesus takes upon Himself the sin of His people (those who will repent and believe) to remove their guilt and punishment before God and transfers His righteousness to them. Sinners are declared righteousness before God and forgiven upon their faith in Christ alone.

 

For whom exactly did the Lord Jesus die?

Jesus died per John 10:11 for the sheep. His sacrifice covers the sins of the sheep. Who are the sheep? Per the recorded words of Jesus in John 10:27-29 the sheep are those the Father gives Him and are marked by hearing the voice of Jesus (the Scriptures) and following Him. Jesus died on the cross for all those the Father chose before time. Jesus sacrifice on the cross while sufficient to cover all mankind’s sins only was only applied to those whom the Father had given the Son. Paul conveys this truth powerfully in Ephesians 1:4-7:

“even as he chose us in him before the foundation of the world, that we should be holy and blameless before him. In love  he predestined us for adoption to himself as sons through Jesus Christ, according to the purpose of his will,  to the praise of his glorious grace, with which he has blessed us in the Beloved.  In him we have redemption through his blood, the forgiveness of our trespasses, according to the riches of his grace,”