It’s true that, technically and traditionally speaking, only religious congregations have/had Third Orders.
Lefebvre would have known that.
Nevertheless, the SSPX statutes provided for 2nd and 3rd Order “members,” which is historically interesting to me:
It seems that, just as in so many other areas of its apostolate and the organization thereof, the SSPX was/is in many respects unique (recall that these Statutes were initially approved by ecclesiastical authority, who likewise would have known Third Orders -at least until then- were only proper to religious congregations, but they seem to have been nevertheless approved anyway. That said, I don’t recall whether the provision for 3rd Order members was included in the original approved Statutes).
It seems that a Society of Apostolic Life is a canonical hybrid, which shares some features of religious congregations (one of which appears to be 2nd and 3rd Orders, and in the case of the SSPX, even “familiars”).
My understanding is that the SAJM (itself modeled upon the SSPX statutes) will also have a 3rd Order soon, and already has Oblates functioning as 2nd Order members).
Once they do, I will join it immediately.