The Prophet Isaiah, seeing far ahead, spoke of the Savior of the world as a lamb who would be slain for the sins of all people.  St. John the Baptist, pointing out the Savior to his own disciples, called him, "the Lamb of God."  In a commentary on the Holy Mass, attributed to St. Isidore of Seville (d. 636), we read:

"Then the priest prays, singing: 'Lamb of God, who takes away the sins of the world, have mercy on us.'  The lamb is said to be innocent because he harms no man or any beast.  And when he is sacrificed, he does not strike at the one killing him, but after he is killed he refreshes his killer.  In like manner, Christ does not strike at anyone.  As the Apostle says: 'He committed no sin, neither was their deceit found in his mouth' (1 Peter 2, 22).  But after his Passion, he refreshed and made believers of many of his converted persecutors  through the communion of his holy Body and Blood.  He himself took away the sins of the world when he forgave us the guilt of our sins.  

"We read that the just and sinners went down into hell before his Passion, and that there was no forgiveness of sins, under the old covenant.  But Christ promised us not only the forgiveness of sins through repentance, but even angelic joy: 'There will be joy among the angels of God over one sinner who repents' (Luke 15, 7).  We pray that Christ, the innocent Lamb of God, who suffered for the salvation of the world, may have mercy on us, saying, 'Have mercy on us.'  Under the old covenant, the lamb was offered for the sins of the people.  Under the New Covenant, Christ offered himself to God the Father that the human race might be freed from sin through his Passion.  And so the 'Lamb of God' is sung at the time when the Body and Blood of Christ is eaten [by the priest], that we may all believe that the Body and Blood of the Lamb -- who took away the sins of the world in his dying -- that is then eaten, grants us eternal life.  This Lamb is Jesus Christ our Lord, who lives and reigns in the unity of the Holy Spirit, for ever and ever.  Amen."

Note that the author mentions that the priest consumes the Body of Christ during the singing of the Lamb of God.  No prayers were said between the Lamb of God and Holy Communion at this time.