Thomas Aquinas Commentary Lamentations 4:20

"The breath of our nostrils, the anointed of Jehovah, was taken in their pits; Of whom we said, Under his shadow we shall live among the nations." — Lamentations 4:20 (ASV)

Fourth, he excludes the protection of kings: the breath of our mouth, by which we breathed in the midst of our anguish; Christ the Lord, Josiah, is taken, for he was killed by the Egyptians (2 Kings 23:29); for our sins, because he himself was just.

Alternatively, this can be explained as referring to Zedekiah, according to what follows in the history. Better still, it can be understood as referring to Christ, for He was wounded for our iniquities (Isaiah 53:5).

The phrase Under your shadow refers to protection, as in the verse, I sat down under his shadow, whom I desired (Song of Solomon 2:3).