The Basilica of St John Lateran is the Pope's Cathedral as bishop of Rome. The Opening Prayer of today's Mass equates "living stones" with "your chosen people," thus indicating one of the themes of today's celebration and one of the reasons for celebrating the Dedication of the Basilica.
The image of "living stones" to describe God's people goes back to the First Letter of Peter. Jesus is the "living stone, rejected by men but chosen by God and precious to him". Peter's use of the image goes back to Jesus himself [Mt 21:43], as he quotes Psalm 118:22-23, that the stone rejected by the builders has become the keystone. Peter then encourages us to set ourselves close to Jesus and so become living stones building a spiritual house.
The reading from Saint Paul uses the same image of building. Our whole life is like a building erected on the foundation stone which is Jesus. Paul then adds another image: each one of us is a "temple of God, a place where the Spirit of God dwells."
Celebrating the dedication of the Pope's Cathedral, we remember that the Church is really the chosen people of God, united with the Pope as the Vicar of Christ.
Father in Heaven, grant that we will always be precious in Your eyes and closely united with Your Son.