False.  +Lefebvre provided and recommended conditional ordination as a matter or routine, with the rare exception of some recalcitrant like Mr. Stark.

This "investigation" nonsense is absurd, since it's based on the claim that the New Rite is valid or invalid based on the intention of the bishop who's performing the ordination/consecration, and yet intention is a matter of the internal forum and cannot be "investigated".  It's just nonsense, and there was never any investigation in the SSPX through the death of Archbishop Lefebvre.  I know, since I was a seminarian in the late 1980s through his death, and knew and had direct conversations with Bishop Williamson and most of the priests in the SSPX at the time.  They did it routinely without any investigation and highly recommended it to every priest that came over from the NO, if for no other reason that to maintain peace in the consciences of the faithful.

You're retrofitting the "investigation" nonsense that later developed in SSPX as they cozied up to Rome onto +Lefebvre.

You don't have to believe they're "always invalid", only that they're postively doubtful.  That suffices, so this is a false dichotomy you're throwing out there.

In fact, the neo-SSPX have refused to conditionally ordain some priests who had asked for it ... because they don't want to ruffle the feathers of the Modernists in Rome.

https://www.cathinfo.com/the-library/fr-calderon's-2014-study-on-the-new-rite-of-episcopal-consecration-in-english/

In 2014, Fr. Calderon's conclusion of the validity of the rite, was this:


...As for the practical attitude to be taken with regard to the new Episcopal Consecrations, the one that the Society has maintained up to now seems to us to be justified:
1. The very probable validity of the rite seems to us to make it morally acceptable to occasionally assist at the Mass (traditional rite) celebrated by a priest or a bishop ordained or consecrated in the new rite, and even to receive Communion therein; it seems to us acceptable, in case of necessity, to receive absolution from them; to treat them as priests and bishops and not as laymen in costume; it seems to us acceptable to allow them to celebrate in our own houses. For the shadows that hover over the validity of their priesthood are but shadows and in all these activities our responsibility is not engaged concerning their exercise of the priesthood. And the remote risk that one communion or one absolution may be invalid is not so serious.
2. But the positive and objective defects from which this rite suffers, which prevent our having certainty of its validity, it seems to us - until there is a Roman judgement, for which many things would have to change - justify and make necessary the conditional reordination of priests ordained by New Bishops and, if necessary, the conditional reconsecration of these bishops. Such doubts cannot be tolerated at the very root of the Sacraments (33).
Father Alvaro Calderon


But to add to this discussion, Fr. Gregory Hesse (canon  +RIP), asked + Lefebvre if his ordination (1981) was OK...I think a real bishop used the new rite of ordination, and everything was done in Latin.  + Lefebvre said his ordination was valid...?? 
Probably assessed that the Intention of the old bishop was correct:  To do what the Church does.
But my two cents worth is : In the new rite, there is no mention of offering the sacrifice of mass for the DEAD. Anyone who refuses to believe that constant teaching of the Church is condemned, according to the Council of TRENT.

CANON III.--If any one saith, that the sacrifice of the mass is only a sacrifice of praise and of thanksgiving; or, that it is a bare commemoration of the sacrifice consummated on the cross, but not a propitiatory sacrifice; or, that it profits him only who receives; and that it ought not to be offered for the living and the dead for sins, pains, satisfactions, and other necessities; let him be anathema.

Novus Ordo Rites are evil, since they generally, and I mean 95% !!! lack something of either the Matter, the Form, and the Million dolors question:  THE INTENTION  !!?

The same routine conditional adminstration of the sacrament apllied to Confirmation as well. In the 1980s, every SSPX seminarian who had been confirmed by a Novus Ordo bishop or priest using the new rite with Chrism consecrated with the new rite was reconfirmed sub conditione.