The format for the Lessons & Carols was created by Bishop Edward White Benson, when he was the brand new Bishop of Truro (a newly created diocese, ca. 1877). He wanted to establish some "traditions" for the new diocese. The original format had 9 lessons, but we've kept to seven here. King's College, Cambridge, still keeps to nine, as do most of the English cathedrals. King's is the one the BBC usually broadcasts live each year. The Bidding Prayer is basically that composed by Bp Benson. . . .As far as I can tell, the dicasteries had something like a dozen people on this thing, and they managed not to think of the Advent festival of lessons and carols. Given the history Fr Kelley gives, this is an authentic treasure of the Anglican spiritual patrimony.
So, no, the Lessons & Carols isn't found in the Ordinariate sources; but there's no reason why it shouldn't be incorporated in some future edition. It is very flexible, in terms of what can be incorporated, both in the lesson selection, and in the musical opportunities. The Magnficat is not a "standard" part; but given the Visitation Gospel lesson, which is an alternative in the lists, it seemed perfectly appropriate to include a Magnificat said to be one of Pope Benedict's favorites, & to do it as a Solemn Magnificat, in the best St. Mary's tradition.
UPDATE: A visitor notes,
The service known as “Lessons and Carols” does not have a rite in the Anglican Book of Common Prayer, either, and thus does not have status as liturgical prayer even within the Anglican tradition.However, worthwhile as such a service can be, so far, I note that nothing is being said about it this year by the people at the Anglicanorum Coetibus Society blog. A good question would be how many OCSP communities are holding this at all.
Since “Lessons and Carols” does not involve any sacrament, there is nothing that precludes any Catholic parish or other congregation from holding such a service. Canonically, “Lessons and Carols” is a pious devotion.