Understanding the Liturgical Worship Service: Service of the Sacrament Part III

Prayer of Thanksgiving/Eucharistic Prayer

Historical: This is a prayer that was once in the Divine Service, then taken out, then re-introduced ignorantly and incorrectly in LBW, before be properly re-introduced in the LSB. I'm not going to go into the details here, though; suffice it to say that there is nothing to be afraid of in the LSB version of prayer of thanksgiving.
Explanation: Thanking God for His Holy Supper. The prayer is essentially a retelling of God's Salvation History, and historically can get pretty lengthy. It is often adapted to fit the liturgical season/holiday, as well, focusing on whatever particular event is relevant. The practice of re-telling important tales goes back to Hebrew/Old Testament culture and so the Prayer of Thanksgiving is merely an extension of that practice.
Also note: LSB's version also includes a bit where we ask God that we worthily receive His body and blood, replacing the Exhortation, which I'll discuss later.
(The word 'Eucharist' comes from the Greek word for 'thanks' and it's because of this prayer that some call the Lord's Supper the 'Eucharist.')
Sacramental: We tell back to God what He has told us in His Word.
Scripture: Matthew 26:6
Alternative: a bunch of DS settings exclude this
Hymns: no

Exhortation

Explanation: A number of hymnals (especially older ones, but also the ELH) include this. Taking Paul's warning that one should examine one's self before eating and drinking our Lord, this is basically a just that: an review of the fact that we are sinful beings in need of God's mercy and forgiveness, which we receive in Jesus' body and blood. Most LCMS congregations either hope that folks do this on their own, or they hope that folks pay attention to the Prayer of Thanksgiving.
Please don't think that I'm condemning the (compilers of the) LSB; nor am I condemning congregations that leave Paul's exhortation up to the members. I'm simply saying that this is an historical part of the Lutheran Divine Service and that it's not 100% wrong. I think the LSB did a fine job of keeping the exhortation in mind, both in the "Prayers for Worship" on the inside cover, as well as in the Prayer of Thanksgiving.
Sacramental: We examine ourselves.
Scripture: I Corinthians 11:27-29
Alternative: LSB inside cover
Hymns: a bunch of hymns ask God that we worthily receive His body and blood, but these are more appropriate during Communion than before, really

Lord's Prayer

Explanation: I'm going to skip over the meaning of Jesus' words and just talk about their relationship to the Lord's Supper.
Our Father in Heaven: we acknowledge that God is in heaven (despite what some think)
Let Your Name be hallowed: His Name is hallowed when His people do what He says: like eating and drinking His flesh and blood.
Let Your kingdom come: We are about to sing the song of all the company of heaven, and feast on Christ, the Lamb of God. This truly is "heaven on earth."
Let Your will be done on earth, just like it is done in heaven: "This do in remembrance of Me."
Give us today our daily bread: Um, pretty self-explanatory
And forgive us our guilts, as we have forgiven or guilters: "Shed for you for the forgiveness of all your sins."
Save us from trial/temptation/accosting, but allay us of evil: what is more refreshing and enlivening than Jesus' body and blood?
Yes, folks, there is a reason this prayer is not said along with all the other prayers.
Scripture: Matthew 6:9-13
Alternatives: I'm sure there are contemporary songs on the Lord's Prayer. (Please don't sing that schmalzy one from the 40's?- it's awful and anyone without gray hair probably despises it.)
Hymns: LSB 957-959; there are others, too