Which version of the Divine Office? Pre-Vatican II, and in the current monastic rite, there are no introductory rites, no doxologies at the end of the psalms, no responsory, no hymn; instead of the responsory, the antiphon "Christus Factus est" (basically the same as the Gradual used at Mass on Psalm Sunday) is chanted, the Pater said in silence, and lastly no concluding rites. So no Benedicamus Domino.
For the current Roman Office, none of the chant books I have (Les Heures Gregoriennes and Antiphonale Romanum II) specify which one to use. Given the history of the Divine Office, I would think it appropriate to omit it during the Triduum, even if you do the rest of the concluding rites.
@Vilyanor: Prior to the 1955 Holy Week reforms, Holy Saturday Vespers was a brief add-on to the Vigil Mass, which was celebrated early in the day unlike now. Which means by that point Vespers was First Vespers of Easter. And since it was attached to the Mass, it was the dismissal of Mass that was used.
After 1955, the Vigil was moved to Holy Saturday night, and Vespers became Vespers of Holy Saturday; there is no First Vespers of Easter, the Triduum being one continuous liturgy. Since you will celebrate the modern Liturgy of the Hours, then yes, Holy Saturday is treated like the other offices in the Triduum. I checked in my monastic antiphonary (2005) and there are no opening or concluding rites for Holy Saturday Vespers. However, the LOTH doesn't follow this. The only vestige of the old practice that I can see in the rubrics is the use of the gradual "Christus factus est" instead of the responsory after the reading.
However the Benedicamus Domino is more or less optional in the LOTH, so again I think it would be OK to omit it.
FWIW, in the old office, Lauds on Thursday, Friday, and Saturday ended with the Christus factus est, a silent Pater noster, and a collect, without the Benedicamus Domino.
FFR, one skips Vespers if attending the Good Friday liturgy and the Easter Vigil.
It is rubbish that Easter is now the only Sunday (and feast of the Lord, I think) without 1st Vespers. My parish apparently sang the old First Vespers during Holy Communion. I was in Rome, so we did that at Ssma. Trinità, which is allowed to use the pre-1955 liturgy with some modifications.
For the Easter Vigil, it is Compline that is skipped for those attending the Vigil. Holy Saturday Vespers is still mandatory for those bound to the Office. For Good Friday, it is Vespers that is skipped by those attending the Good Friday liturgy, but Compline remains required for those bound.
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