Good topic and so appropo for the churches to discuss.
Just some off the top of my head comments. Under the machinations or workings of the law which operates for the most part in a "you-scratch-my-back-and-I-in-return-scratch yours, we act toward one another seeking to equal out an indebtedness placed upon us. For example, to get food items for my family I must pay for them at a grocery store. "I give to you as you give to me" like the oldies song goes. In other words if I want a relationship with you (under the law) I'll give my attention to you but you have to listen in order to get my attention. It happens in a vice-versa sort of way.
In another example, in order to drive to get my groceries I have to place myself under the civil laws when I drive in public. I'm not out there driving by myself but there are other people out there doing the same thing for themselves and their families. I'm placed in a situation of indebtedness to others so that should I run over someone with my car as I drive, I am indebted to pay for their medical expenses and a lawyer if I get sued. I also become indebted to the lawyer to pay a retainer for his/her services.
The common denominator is that I have placed myself indebted to others in order to make things right and to equal out any indebtedness to others. I need food. I must pay for food (so the others get paid for making and delivering the food) in order for me to get food. Here's another example: If I hit you, you have a right to hit me back in order to equal out the indebtedness. It never ends under the law as we live under the law with and among others who live this way in their lives also.
It is a matter of living under the effects/affects of the law. It usually has to do with living life among others, ie. neighbors or others (that is another topic for review: who is my neighbor vs. the general public).
Under God Himself, He give good things to us everyday. He gives me constant breath and if I choose only to live under the law I am indebted to give thanks to Him for each breath given. See first article of Creed: ...I am indebted (German, schuldig) to God to give thanks to Him for everythign at each moment. A crushing burden is placed upon me for all these gifts. But the creed does not leave us to live under indebtedness and its crushing load of guilt for not paying it back. The creed is not just the first article. There are two more. THe next one is the kicker: 2nd article, God has given Jesus his Son to take upon Himself that indebtedness of ours and in its place God gives us what Jesus has received new life, freedom from death, etc.
Under the Gospel (which supplants life under the law with all its indebtednesses) Jesus actually takes all of that indebtedness upon Himself and takes it off my shoulders/the indebted one. Jesus as the Suffering Servant takes upon Himself my sin (indebtedness) and puts it to death in His Body on the/His cross. Under the Gospel we have actually become free of the crushing load because Jesus has taken that upon Himself and away from us.
However as sinners we still must suffer the indebtedness as we continue to live here but now not alone but as a Christian, with the One who has already gone to the cross with our indebtness/sin. Having been connected to Christ's Living Body of which we are members, through the sacraments and faith, Christ has indeed taken away the sin/indebtedness and in return has given us eternal life with God/Himself/Christ.
I have a way of teaching Luther's Small Catechism which invites the student to first look at part one, ie. God's Law (the Decalogue) from the standpoint of how we will learn to understand God's law first as what God's demands that we do for justice reasons, in general. Then we talk about how Christians understand God's law as Jesus applies it. And then how St. Paul shows us what effects are created by the law as it acts upon oneself in one's life to see how it places us seriously under conditions of heavily applied indebtedness to create burdens on our life lived for justice effects/affects alone. We are debtors to our neighbors under the law. Justice seeks ways to make things right under the law through the satisfaction of indebtedness to others living under the law. But this equaling out leading toward freedom from indebtedness never is enough to fulfill and exhaust within all arenas of living among others. When one case is equaled out another one raises its head. On and on it goes. We search for lasting justice only found under living life and trusting what life gives us under the law. But of course for Christians we discover that living for life under the law is to live under a curse (see Galatians 3)
"...with the law comes the knowledge of sin/indebtedness." (taking liberties with the biblical text/Romans here)
God's law cannot exhaust the demand for justice because there is always more to pay for and to be paid for by trusting how the law operates for us and for the neighbor.
However in Jesus' cross ALONE does this neverending conundrum of satisfaction of indebtedness end and exhaust itself. Christ's death ALONE silences the voice of the law with its accusations and demands. He takes away the sin of the world through His Body.
All this is then taken up as the student moves from the Law portion of the catechism into the 2nd part of the catechism ie. the unique Gospel or the Creed. Luther's meanings in article one and then article 2 deal with these issues of indebtedness and Christ's freeing us from this indebtedness through his death on the cross. It's all there in the German version and the word, schuldig.
Notice: We haven't gotten further than this if we don't then talk about the new life in the resurrection and life in the Body of Christ through His resurrection for us. What comes after the resolution of indebtedness isn't justice (that was dealt with in Christ's death, it was fulfilled and then set aside). What comes next is new life not based on the law and its effects (because Christ has set them aside in his death.) His life provides something new or else Easter, the Ascension and Pentecost would be meaningless if there wasn't more than satisfaction for sin, more than Good Friday (Karfreitag)
Some scriptural references for this unique and one-off turn into new life in Christ following his death:
1. Romans 5
2. Romans 3
3. 1 Corinthians 15
et. al.