Cyril of Alexandria

The law also ordered, that those who were cleansed from leprosy should offer sacrifice for the sake of their purification. Whereby the Jewish priests who were jealous of His glory might know that it was by Christ granting them health that they were suddenly and miraculously healed.

Catena Aurea by Aquinas ↗

Theophylact of Ohrid

He commands them to show themselves to the priests. For the priests examined such people, and from them they received the determination of whether they were clean from leprosy or not (Lev. 13). The priests had signs by which they identified incurable leprosy. And even when someone had contracted leprosy and then recovered, the priests would examine them, and the gift commanded in the Law was brought to them. …

Commentary on Luke ↗

Bede

When he saw them, he said: Go, show yourselves to the priests. And it happened as they went, they were cleansed. The Lord is found to have sent none of those to whom he granted these corporal benefits to the priests, except lepers, because evidently, the priesthood of the Jews was a figure of the future royal priesthood, which is in the Church, whereby all belonging to the body of Christ, the highest and true Prince of priests, are consecrated. …

On the Gospel of Luke ↗

Bonaventure

Third, as to the ease of the manner of healing, he adds: Whom when he saw, he said: Go, show yourselves to the priests. For the judgment of leprosy pertains to the priests, according to that saying of Leviticus 14: "The leper, when he is to be cleansed, shall be brought to the priest," etc., through the entire chapter. …

Commentary on Luke, Chapter 17 ↗