I think the most detailed official description of the ceremony is found in
Ceremonial of Bishops, 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.”
“226 After the introductory rites (consisting of a song, greeting, and prayer), one or more readings from Sacred Scripture are proclaimed, with songs or psalms or intervals of silence interspersed. The readings are explained in a homily that relates then to the lives of those present.
The homily may be followed by a period of silent reflection on the word of God. Then the whole congregation with one heart and voice should join in praying the intercessions, in litanic or other suitable form that encourages participation. Finally, the Lord’s Prayer should be recited.
The bishop, as the one who presides over the assembly, concludes the celebration with a prayer and blessed the people in the manner indicated in nos. 1120-1121.
One of the deacons or ministers dismisses the people, saying
Go in the peace of Christ, and all reply,
Thanks be to God.”
Also instructive from
Ceremonial of Bishops comes under the heading “Institution of Readers within a Celebration of the Word” in n. 805: “the celebration may begin with the singing of an antiphon or some other suitable song; then the opening prayer of the Mass for the ministers of the Church may be said. The liturgy of the word is carried out as at Mass and with suitable responsorial psalms or other songs between the readings.”
With a lay person leading I think they should follow this part of the
General Instruction of the Liturgy of the Hours “258 When there is no priest or deacon, the person who presides is only one among equals; he does not enter the sanctuary, nor does he greet or bless the people.” If being out of the sanctuary is not practical, then do not use the chair the Priest would use. The “does not greet” instruction means not saying “The Lord be with you.” The blessing at the end would be as in the Liturgy of the Hours or
Holy Communion and the Worship of the Eucharist Outside of Mass for a lay person leading. The lay person would not use the orans posture. A lay person would not kiss the altar, even if he were putting the Book of the Gospels on it, following the instructions in that book.
It does not include the penitential rite. That would be included if there was a distribution of Communion, following
Holy Communion and the Worship of the Eucharist Outside of Mass.
The General Instruction of the Liturgy of the Hours is at
https://www.liturgyoffice.org.uk/Resources/Rites/GILH.pdf
[Excerpts from
Ceremonial of Bishops © 1989, International Commission on English in the Liturgy Corporation. Excerpt from
General Introduction on the Liturgy of the Hours English translation © 1974, the Hierarchies of Australia, England and Wales, Ireland. All Rights Reserved.]