To whom was Isaiah referring in Isaiah 53?

In prophetic recapitulation, the story of Christ is told repeatedly in many ways. Noah in the ark, Moses and the ark of bulrushes [1], the tablets of the law in the ark of the covenant are all prophecies of Christ. Using this principle A, B and C prophesy D. If an author is aware of A but not B, C or D he can write of A and appear to be prophesying of B and C, while it is God's intent to speak of Christ, (D).

A, B, and C will have enough elements to be referring to each other, but the apostles never use such references. They always use A, B and C to speak of Christ. An example of this is found in Matthew 2, where references to Moses's birth, Israel's exodus, Abraham's sojourn in Egypt, and Joseph ben Israel taking God's son, Israel, into Egypt all are intermingled.

Isaiah may have been writing of Zedekiah, Jeremiah, or even Uzziah, while God was writing of Christ.

[1]Ex 2:3 And when she could not longer hide him, she took for him an ark of bulrushes, and daubed it with slime and with pitch, and put the child therein; and she laid [it] in the flags by the river’s brink.