This sort of logic means that no Pope has the authority to excommunicate anyone as a schismatic, since schism depends on the interior state of a person.
For although Liberius was not a heretic, nevertheless he was considered one, on account of the peace he made with the Arians, and by that presumption the pontificate could rightly be taken from him: for men are not bound, or able to read hearts; but when they see that someone is a heretic by his external works, they judge him to be a heretic pure and simple, and condemn him as a heretic. (St. Robert Bellarmine)
No. The Pope did not excommunicate anybody. He was saying in a letter that an automatic excommunication--a latae sententiae excommunication--had taken place. In other words, he believed Lefebvre had excommunicated himself by disobeying. And he said this was because of schism. On both counts he was wrong. They were assumptions he had no way of actually knowing. Whether the automatic excommunication took effect depended on the interior state of Lefebvre--his motives for disobedience. They were, in fact, according to the highest principles of the Catholic Church--and in so doing the Archbishop evoked a canonical exception that was perfectly legitimate. Facts are facts.
"This sort of logic means that no Pope has the authority to excommunicate anyone as a schismatic, since schism depends on the interior state of a person."
Not true. A papal tribunal in which charges are made and subjects are duty-bound to respond and to defend themselves usually had been the proper forum in the past for high churchmen. The modernists were too clever for this, though. Archbishop Lefebvre had the whole of Catholic Tradition on his side. It would have been counter-productive to openly charge him with schism in a tribunal in which he might properly defend himself and prove beyond a shadow of a doubt that he was innocent. So Lefebvre's enemies--which included the Pope--decided on the automatic excommunication, by first giving him the runaround on the business of the consecrations until he had no other choice but disobedience or surrender to the new doctrines.