• and gave it to them,
saying, "This is my body, which is given for you.
Do this in remembrance of me."
20 • And likewise the cup after they had eaten,
• saying, "This cup that is poured out for you
is the new covenant in my blood.
On the night in which he was betrayed Jesus took two elements of the Passover seder and made of them a new feast of commemoration. Luke's account of what happened at the Last Supper has to specify which cup from the Passover seder was the one that was taken up to be perpetuated in the Lord's Supper celebration because Luke, uniquely of the gospels, talks about the vow of separation that Jesus took during the feast in terms of the cup that he shared among the disciples before the breaking of bread. The cup that was used to inaugurate the feast of the Lord's Supper was specifically, 'the cup after they had eaten.'
At the original Passover, when God was visiting the tenth plague upon the Egyptians, those who were gathered together to eat the Passover were sheltering within houses where the blood of the Passover lamb had been placed on the lintel and the doorposts as a sign that those inside were to be separated from the plague because God had made a covenant with them. Now as this feast and it's meaning was renewed, the cup of wine became the symbol of the blood that would be shed to secure the renewed covenantal relationship for all time.
In taking this cup generations of believers share the fellowship of Christ in the kingdom of God, made holy in their sharing because of the holiness of the 'Lamb of God' who was separated out to be our Passover, to fulfil his vows and to complete the work that God had given him to do.