The Rite of Penance describes various ceremonies, some having no priest. The General Introduction includes: “37. … Penitential services, moreover, are very useful in places where no priest is available to give sacramental absolution.” So obviously if it this ceremony, with no priest or deacon, then it is O.K. for a lay minister to read the Gospel.
But a “communal reconciliation service” sounds much more like the “Rite for Reconciliation of Several Penitents with Individual Confession and Absolution” where there is a priest. In this situation it is incorrect for a lay reader to proclaim the Gospel. The ceremony description includes:
“CELEBRATION OF THE WORD OF GOD
51. The celebration of the word follows.”
Another book, “Ceremonial of Bishops” gives more information about a Celebration of the Word of God in Part III, Chapter 7: “CELEBRATIONS OF THE WORD OF GOD”. This includes: “224. Celebrations of the word of God should be patterned on the structure of the liturgy of the word at Mass.”
Another part of the book, Ceremonial of Bishops, Part I, Chapter 4, “GENERAL NORMS”, section II “SIGNS OF REVERENCE IN GENERAL” has:
“Revence toward the gospel
74. While the gospel reading is being proclaimed at Mass, at a celebration of the word, and at a prolonged vigil, all stand and, as a rule, face the reader.
The deacon solemnly carrying the Book of the Gospels to the ambo is preceded by the censerbearer with the censer and acolytes with lighted candles.
At the ambo the deacon stands facing the people and, with hands joined, says the greeting; …
In the absence of a deacon, a presbyter asks for and receives a blessing from the bishop, and proclaims the gospel reading in the way just described.”
So there are detailed instructions here for how the Gospel is proclaimed in a Celebration of the Word, and it is the same way as at Mass.
So in a Celebration of the Word the Gospel should be read by a Deacon, in the absence of a Deacon by a Priest, in the absence of both by a Bishop, in the absence of these by an Instituted Reader, in the absence of all these by another lay reader.