Theophylact of Ohrid

The spreading of garments seems to signify that those worthy to praise Jesus, having put off the old man, lay him down and subject him to Jesus, so that by treading upon him He might sanctify him, and so that the flesh would not rise up against the spirit, so that they themselves might also say: "Submit to the Lord and hope in Him" (Ps. 36:7).

Commentary on Luke ↗

Bede

And as he went, they spread their garments in the way. As the Lord is carried by the donkey, the disciples lay their garments in the path, because by stripping away their own bodily attire, they prepare the way for the simpler servants of God with their own blood, so that they may walk with an undisturbed step of the mind towards Jerusalem, where Jesus leads. …

On the Gospel of Luke ↗

Bonaventure

Now as he went forth etc. After he showed that he has royal power through his excellence in commanding and the obedience of the disciples in complying, here he shows thirdly through the honor of the people in praising together. To express this, first the devotion of those praising is set forth; second, the loftiness of the praises, at the words: Blessed is he who comes in the name of the Lord; third, the confutation of the envious, at the words: And certain of the Pharisees etc. …

Commentary on Luke, Chapter 19 ↗