I have a general take on the Lord’s/Last Supper: the Synoptic Gospels depict Jesus predicting his death as the pathway to his Messianic enthronement. This cross-shaped life is also the call to Jesus’ followers: take up the cross and follow.
In addition, you might start probing the significance of rewriting the Passover ceremony around Jesus, such that the “ransom saying,” (the Son of Man did not come to be served but to serve and to give his life as a ransom for many) is illustrated in the meal. The body of Jesus is given in order that we might be set free and might become the New Covenant people of God. Taking and eating is our participation in [the people of] this deliverance.
All this from some combination of Matthew and Mark, perhaps with a little Paul thrown in if I’m honest.
But what’s going on in Luke?
One thing, at least, is definitely different in this telling of the story of the supper itself. A cup is passed before the bread.
Another interesting choice Luke makes is to put the disciples’ dispute about greatness here. Whereas in Mark this happens on the way to Jerusalem, after a passion prediction, Luke locates the fight in the upper room after they’ve taken the Supper.
This is even more interesting in that Jesus’ response to the disciples here is part of the talk he gives them that culminates in the ransom saying. But Luke eliminates the ransom saying. He substitutes a more generalized call to imitate him, who is in their midst as a servant.
Finally, this is followed by another lesson from Jesus: the disciples are the ones who remain with him in suffering, and therefore receive from Jesus the same kingdom that Jesus receives from the father–its food, its drink, and its rule (you will sit on twelve thrones judging the twelve tribes of Israel).
What are we to make of all this?
First, Bart Ehrman has famously argued that the interpretation of the bread (“which is given for you”) and the “second cup” are not original to Luke, but later insertions to bring the passage into conformity with the other Synoptic Gospels.
Although the manuscript evidence for this is weak, it works really well with the passage as a whole.
With the removal of the ransom saying in particular, the idea of Jesus dying “for you” is muted, and the notion that Jesus dies as an example and in order to bring about a surprising sort of divine reign is drawn to the forefront.
By placing here the saying about Jesus as servant to be imitated, without ransom, participation in the supper is drawn more in the direction of finding our own lives drawn to self-giving service.
By following that with the definition of the twelve as “those who remain with Jesus in his sufferings,” and thereby receive the kingdom, the imitative note is struck even more forcefully.
Why take the cup? Why drink the bread?
Here, the most clear reason is to remember that Jesus received the kingdom through suffering, and that self-giving life in service of others is the call of discipleship.