“At the end of the hours, when the Concluding Prayer is read/sung, does the lay leader say the words “Let us Pray” before reciting the prayer?”
My understanding is that the lay leader does say these words. In the Divine Office (approved in 1973 for England) it has on page “[8]”.
“The concluding prayer is prefixed with Let us pray when said at The Office of Readings, Prayer During the Day and Night Prayer. At Morning and Evening Prayer it is said after the Lord’s Prayer, without introduction.”
So, depending on the prayer, it is said or not said. But there is no suggestion that it is said, or not said, depending on whether there is a lay leader or an ordained leader.
On page “[14]” of this book it gives the different blessings, depending on whether the leader is lay or ordained.
“Secondly, what would be the correct posture for the lay presider when he says the prayer? Would his hands be folded or would he extend his hands (the orans posture)?”
My understanding is that the orans posture is not mentioned in the General Introduction to the Liturgy of the Hours (GILH). It is mentioned in Ceremonial of Bishops, Part III, “Liturgy of the Hours and Celebrations of the Word of God.”
“205 The Lord’s Prayer is sung or said by all, and, if the bishop so decides without an introductory invitation.
With hands outstretched, the bishop sings or says the concluding prayer. All reply, Amen.”
In the Directory for Sunday Celebrations in the Absence of a Priest (2 June 1988 Congregation for Divine Worship) it has:
“39. A layperson who leads the assembly acts as one among equals, in the way followed in the liturgy of the hours when not presided over by an ordained minister, and in the case of blessings when the minister is a layperson (“May the Lord bless us . . .”; “Let us praise the Lord . . .”). The layperson is not to use words that are proper to a priest or deacon and is to omit rites that are too readily associated with the Mass, for example, greetings - especially “The Lord be with you” - and dismissals, since these might give the impression that the layperson is a sacred minister.” Footnote 33: See GILH, no. 258: DOL 426, no. 3688; see also The Roman Ritual, Book of Blessings, nos. 48, 119, 130, 181.”
(DOL is a book Documents on the Liturgy 1963-1979, which includes the GILH.)
Book of Blessings n. 130 is a blessing for a married couple. It has “A lay minister concludes the rite by signing himself or herself with the sign of the cross and saying …”. This contrasts with n. 129 “A minister who is a priest or deacon concludes the rite by first blessing the couple and saying, with hands outstretched toward them.” There are also different prayers for the lay minister.
So what is the correct posture for a lay leader for the concluding prayer? The instructions are not particularly clear. But my interpretation would be not to use the orans posture, since there is not direction to do so in the GILH. It is not clear that the instruction to do it in the Ceremonial of Bishops applies to a lay leader.