In the General Instruction of the Liturgy of the Hours, there are no particular norms (rules) for which ending or formula you may use to conclude the Prayer of the Day with.
That said one is free to use the concluding formula of one's choice. The concluding prayer has several options to end the prayer and although the formula "through our Lord Jesus Christ your Son, who lives and reigns..." is not formally mentioned as an alternative ending, in your edition, this traditional form may still be employed. I personally use the long formula when I pray the Divine Office or the Liturgy of the Hours.
Thus there are four ways to conclude the Prayer of the Day. Whoever recites the final prayer in a congregation has the privilege of using his choice of ending, whether a priest, deacon or lay person.
Here are the norms for the Concluding Prayer:
The concluding prayer at the end marks the completion of an entire hour. In a celebration in public and with a congregation, it belongs by tradition to a priest or deacon to say this prayer.
In the office of readings, this prayer is as a rule the prayer proper to the day. At night prayer, the prayer is always the prayer given in the psalter for that hour.
The concluding prayer at morning prayer and evening prayer is taken from the proper on Sundays, on the weekdays of the seasons of Advent, Christmas, Lent, and Easter, and on solemnities, feasts, and memorials. On weekdays in Ordinary Time the prayer is the one given in the four-week psalter to express the character of these two hours.
The concluding prayer at daytime prayer is taken from the proper on Sundays, on the weekdays of the seasons of Advent, Christmas, Lent, and Easter, and on solemnities and feasts. On other days the prayers are those that express the character of the particular hour. These are given in the four-week psalter.