Theophylact of Ohrid

Having said this and that they will be hated and some of them will be put to death, He adds the greatest consolation: "not a hair of your head shall perish." You, He says, will be saved, and not the slightest part of you shall perish, even though to many it will seem that it has perished; only one must endure.

Commentary on Luke ↗

Augustine of Hippo

Death comes to either the soul or the body. The soul cannot die, and yet it can die. It cannot die, because its consciousness is never lost. It can die, if it loses God. You see, just as the soul itself is the life of the body, so in the same way God is the life of the soul. As the body dies when the soul that is its life abandons it, in the same way when God abandons the soul, it dies. To make sure, however, that God does not abandon the soul, it must always have enough faith not to fear death for God's sake. …

Sermon 273.1 ↗

Gregory the Dialogist

But because the things foretold concerning the affliction of death are harsh, consolation is immediately added concerning the joy of the resurrection, when it is said: "Not a hair of your head shall perish." We know, brothers, that flesh when cut feels pain, but hair when cut does not feel pain. Therefore He says to His martyrs: "Not a hair of your head shall perish," clearly saying: Why do you fear that what feels pain when cut may perish, when even that which does not feel pain when cut cannot perish in you?

Forty Gospel Homilies, Homily 35 ↗

Bede

And not a hair of your head will perish. We know that flesh cut feels pain, hair cut does not feel pain. Therefore, he says to his martyrs: Not a hair of your head will perish, evidently saying openly: Why do you fear lest what is cut and feels pain will perish, when even that in you which is cut and feels no pain cannot perish? …

On the Gospel of Luke ↗