I think they sang enough variations or substitutions for “Lamb of God” to allow all the eucharistic ministers time to get situated. At our parish, they start coming up during the sign of peace, but there are often 8 or more, and if the Lamb of God ended early, well we would have to sit in complete silence for a moment or two (the horror).
Reference GIRM 83:
The Fraction
83. The priest breaks the Eucharistic Bread, assisted, if the case calls for it, by the deacon or a concelebrant. Christ’s gesture of breaking bread at the Last Supper, which gave the entire Eucharistic Action its name in apostolic times, signifies that the many faithful are made one body (1 Cor 10:17) by receiving Communion from the one Bread of Life which is Christ, who died and rose for the salvation of the world. The fraction or breaking of bread is begun after the sign of peace and is carried out with proper reverence, though it should not be unnecessarily prolonged, nor should it be accorded undue importance. This rite is reserved to the priest and the deacon.
The priest breaks the Bread and puts a piece of the host into the chalice to signify the unity of the Body and Blood of the Lord in the work of salvation, namely, of the living and glorious Body of Jesus Christ. The supplication Agnus Dei, is, as a rule, sung by the choir or cantor with the congregation responding; or it is, at least, recited aloud. This invocation accompanies the fraction and, for this reason, may be repeated as many times as necessary until the rite has reached its conclusion, the last time ending with the words dona nobis pacem (grant us peace).
Leaving aside the idea of "eucharistic" ministers, the proper action is to repeat "Agnus Dei, qui tolis peccata mundi, misere nobis" as often as needed, not to ad lib.
You most likely mean extraordinary ministers of Holy Communion. As Redemptionis Sacramentum reminds us, only a Priest may be referred to as a Eucharistic Minister. People need to stop blurring the distinction between the Ministerial Priesthood of the ordained and the common priesthood of the believer.
1. The Extraordinary Minister of Holy Communion
[154.] As has already been recalled, “the only minister who can confect the Sacrament of the Eucharist in persona Christi is a validly ordained Priest”.[254] Hence the name “minister of the Eucharist” belongs properly to the Priest alone. Moreover, also by reason of their sacred Ordination, the ordinary ministers of Holy Communion are the Bishop, the Priest and the Deacon,[255] to whom it belongs therefore to administer Holy Communion to the lay members of Christ’s faithful during the celebration of Mass. In this way their ministerial office in the Church is fully and accurately brought to light, and the sign value of the Sacrament is made complete.
Our parish church liturgy has always been very close to the GIRM (General Instructions of the Roman Missal). However, there have been a few exceptions. Now, our Bishop Gerald Barns, not known for being a Traditional Bishop, just gave all the pastors their marching orders which have come down from the Vatican.
A priest or deacon must remove the Holy Communion ciborium(s) from the tabernacle and return it to same. No Extraordinary Ministers can do that.
Extraordinary Ministers are NOT to come on to the altar and stand behind the priest during the Agnus Dei. All EMs are to remain at the foot of the altar and never be on the altar before the priest takes Holy Communion.
There are some other changes as well, such as to where the priest’s chair is to be placed and just who gets to process in and out of Mass with the priest.
For our parish, the changes required will not be all that significant. For the parish next door, which dresses the EMs up in albs and has them march down the aisle with the priest and sit on the altar during the Mass as well as do a few other things, I can just hear the hoots and hollering. In that parish, at the recitation of the Our Father, the pastor invites all of the children at Mass to come up onto the altar. It will be interesting to see how many of these pastors follow the Bishop’s directives.