Oddly, the French LOTH that I use doesn’t have this rubric.
For the psalmody:
(my bold)
I’m not completely certain if this applies to the Gospel canticles as well. My reference for how to recite the LOTH is the Benedictine monks of the abbey I’m affiliated with (although they have some extra rubrics particular to the Rule of St. Benedict, such as the Kyrie and silent Our Father before the collects of the minor hours and Compline, and prayers for the dead and absent brothers after each Office). The general rule they follow is that when an Office is recited (in their case chanted recto-tono),they don’t repeat the antiphon. If it is a sung office (i.e. Lauds and Vespers, and in Latin), then the antiphon is repeated. Since they always sing Lauds and Vespers I can’t say what the rule would be for a recited Gospel canticle. For Compline, in the monastic tradition the office is said without antiphons, including the Canticle of Simeon.
My own opinion is that in recitation, the antiphon need not be repeated, but in a chanted Office, it needs to be repeated for musical consistency; the end of the psalm tone is designed so that it is easy to pick up the antiphon on the right note.
Interestingly, pre-Vatican II it was customary to chant only the first part of the antiphon (up to what would be the * in later antiphonaries) before the psalm or canticle, and then the entire antiphon, after the psalm. Sometime during the reforms under the pontificate of Pius XII, this was changed so that the entire antiphon was chanted before and after the psalmody (and the cantor instead intones the antiphon up to the *, the choir following with the rest). The 1934 Monastic Antiphonary that I have, has the arrangement of singing only the opening of the antiphon before the psalm and the whole antiphon after. The current 2005 Monastic antiphonary has the full antiphon before the psalm, with the * to indicate the part intoned by the cantor).
So in today’s chanting of the psalms in a choir setting, in Latin, the cantor intones up to the star, the choir then picks up the rest of the antiphon, the choir alternates verses throughout the psalmody, and after the doxology the entire choir sings the entire antiphon.