Because this is a mixed congregation of both Jews and Gentiles, one can surmise that Paul’s use of “the law” would be well understood to be those basic provisions of the law (circumcision, Sabbath keeping, food regulations, refraining from worship of idols) that served as identity markers for Jews, and were constant points of contention and division in the early church. Knowing this allows one to see how the unity and actions of love that are outlined and encouraged in chapter twelve of Romans come into play. In addition to that, when considering that this is a letter that will be read to a gathered church at a single sitting, it is worth remembering a very early statement in the letter, wherein Paul uses the phrase “from faith to faith” (Romans 1:17).
This simple statement sees Paul borrowing from the imperial propaganda of the day, which presents Caesar as the supreme benefactor. The statement implies that Caesar is faithful to his subjects, providing them with peace and security, and therefore his subjects are faithful and loyal to him and to Rome. One must hear the words of the thirteenth chapter with such words and thoughts in mind, in the knowledge that Paul is presenting Jesus as the actual supreme benefactor, of which the Caesar is merely a parody. All civic interactions proceed within this framework, and the self-sacrificial love modeled by Jesus which saw Him go to the cross (unconcerned with the shame because of the honor He trusted would come), becomes the model upon which the life of the Christian community is based (unconcerned with shame because of the honor that comes with what counts as the fulfillment of the law, thereby marking one out as a member of the people of the Creator God and a participant in His kingdom).
From here, Paul advances towards the meal table, which it is clear that he has in mind as he goes on to write “Let us live decently as in the daytime, not in carousing and drunkenness, not in sexual immorality and sensuality, not in discord and jealousy” (13:13). Though it is not meant to serve as an accusation, this is language of the portion of the Hellenistic meal referred to as the “symposium” (period of revelry---singing of songs, debates, speeches, etc…---following a meal), and as it is possible that this church is hearing this letter while gathered for fellowship that will include a meal, the language would not be lost on them either. It is to this then that Paul adds “put on the Lord Jesus Christ, and make no provision for the flesh to arouse its desires” (13:14).
A great disservice is done to the apostle if one simply substitutes personal and subjective notions of “the flesh” here, rather than considering “the flesh” within the context of the potential for disunity, division, stratification, and unwarranted authoritarianism within the church, as well as its connotations of the old age prior to the Resurrection, the inauguration of the new creation, and of the kingdom of the covenant God, in which preferring others above oneself is to be the norm.
One must also take this statement into consideration in the context of the dissertation regarding the Christian’s responsibilities towards governing authorities. Because one considers himself or herself to be part of the kingdom of God, a desire of the flesh might be to cast off all restraint and disregard governing authorities. This was obviously a real possibility, which would account for Paul’s insistence that such authorities are “God’s servant for your good” (13:4a), and that it is “necessary to be in subjection” (13:5a) (Note: Though democracies did exist, Paul does not have knowledge of a government that is constituted by “We the people,” such as to be found with the United States of America; so it is incumbent upon all generations of Christians, the world over, to understand Paul’s words in context and then to work out the implications of those words within their own time and place, guided by the dictates of the existing kingdom of heaven.)
Rather than thinking about putting on the Lord Jesus Christ in the context of the cultivation of private spirituality, the understanding of putting on the Lord Jesus Christ should be shaped, and processed horizontally and outwardly, by embodying the transformational, kingdom-of-God-contexted love that was put on display by Jesus throughout the entirety of His mission, culminating in the cross. This would certainly serve to quell any fleshly desires that might be manifested (separations based on honor and shame) or discussed (open rebellion against Rome that could result in the taking up of arms and the discrediting of the Jesus movement) at the meal table, thus resulting in a life of true holiness (a life laid on the altar of sacrifice in service to Israel’s God).