St Augustine's homily on the the feast emphasises the relationship between Laurence's martyrdom and his ministry as deacon:
The Roman Church commends this day to us as the blessed
Laurence’s day of triumph, on which he trod down the world as it roared and
raged against him; spurned it as it coaxed and wheedled him; and in each case,
conquered the devil as he persecuted him. For in that Church, you see, as you
have regularly been told, he performed the office of deacon; it was there that
he administered the sacred chalice of Christ’s blood; there that he shed his own
blood for the name of Christ. The blessed apostle John clearly explained the
mystery of the Lord’s supper when he said Just as Christ laid down his life
for us, so we too ought to lay down our lives for the brethren. St Laurence
understood this, my brethren, and he did it; and he undoubtedly prepared things
similar to what he received at that table. He loved Christ in his life, he
imitated him in his death.
Two things might strike the Anglican mind about Augustine's words. Firstly, "the Roman Church commends this day to us ..." The church at Rome 'commended' - not directed - the church at Hippo ("us") to share in the commemoration of Laurence. This description of the relationship in the patristic era between Rome and the other churches - the primacy of honour - reflects historic Anglican belief.
Secondly, we perhaps get an indication here of why the historic witness of the Roman church should be celebrated by the other churches. It was in a particular, specific way in Rome that the forces of the imperium confronted the church of the Crucified and Risen One. From the martyrdom of Peter and Paul to that of Sixtus II - Laurence's bishop, executed merely days before him - the church at Rome confessed the Cross and Resurrection as the imperium "roared and raged". In celebrating the martyrs of the Roman church such as Laurence, Anglicans are reflecting on the universal Church's call to confess the Cross before Caesar.
The 1662 BCP's commemoration of Laurence - continued in most contemporary Anglican calendars - offers an alternative to the anti-Roman prejudice and rhetoric within Anglicanism. This prejudice and rhetoric was once (but no longer) associated with evangelicalism and is now often present in the more aggressive manifestations of Anglican liberalism. Classical Anglicanism offers a different way, respecting and celebrating the primacy of honour of that church called to walk in the way of the Cross in the city of the Caesars, so that the churches may be renewed in their witness before the contemporary imperium.