If we dug up a lost book by one of the apostles, could it be added to the canon of the Bible or would that be impossible?

It would take an ecumenical council or an ex cathedra statement by the pope to settle the issue definitively (assuming non-Catholics would give either one credence), but it almost certainly would never happen.

The first problem we would have to settle is how to prove, after an absence of so many centuries, that the work in question really was by an apostle or an apostolic man. This in itself would be insurmountable. There is no way that we today could establish that the work was genuine.

The early Church judged which books were apostolic and which were not based on which had been handed down to them as apostolic by Church Tradition. Those books which had been widely handed down as apostolic were regarded as apostolic when the canon was settled in the late 300s.

But by definition we could not apply that test to a manuscript we just now dug up. It is difficult to imagine evidence that could show conclusively that it was written by an apostle rather than by someone pretending to be an apostle. (There were such individuals in the first century, and Paul had to warn against them and give his audience a way to know his letters were genuine; cf. 2 Thes 2:2, 3:17.)

The book would have to be unknown at the time the canon was settled in the 300s, because a negative judgment was passed at that time on all books which were known and were not identified as Scripture. Books not included in the canon by the Fathers of the 300s were rejected as uncanonical, meaning our newly discovered manuscript would need to have been lost before that time.