Whoever serves me must follow me, for where I am, there also will my servant be. St. Lawrence whose memory the Church honors today is celebrated for two things: his care for the temporal welfare of the Church as well as his care and love for the poor whom he served as a deacon in Rome. St. Lawrence joins a long list of the early Church martyrs who gave their lives for their loyalty to Christ and for their love for the Church. Having witnessed only four days earlier the brutal slaying of a pope and four deacons, one would have forgiven Lawrence if he decided to renounce his faith or hand over the properties of the Church as the emperor had wanted him to do. However, he stood firm in his resolve to protect the properties of the Church, a cause for which he got burned alive. The inclusion of his name in the Roman Canon reveals how highly he was regarded in the early Church. Together with saints Peter and Paul, he is venerated as a patron saint of Rome. 
In the Gospel reading for today, Jesus reminds his disciples that as servants, their destiny is intertwined with his. As a matter of fact, a faithful carrying out of their responsibility as his servants would see them take their place by his side (be with him where he is). While sometimes we interpret this as a reference to the fate that befell the martyrs- which is valid by all accounts, I also think that the destiny to which Jesus referred is his glory. Jesus’ glory consists in seeing Jesus as he really is (cf. I John 3:2). The martyrs gave their lives because of their belief that in baptism, one is joined to Jesus Christ such that the life after baptism is that of Christ himself.
The martyrs also gave their lives as an act of generosity. They were aware that as they were being led towards their deaths, there were many of their brothers and sisters who were watching, some of whose faith needed strengthening. For the sake of such brothers and sisters of theirs, they had to be brave. Like Jesus, they were to be willing to give their lives for their brothers and sisters. Like a grain of wheat that only bears fruit when it falls on the ground, the blood of the martyrs watered the ground for the spread of the faith.