Lamentations comes after Jeremiah because it has traditionally been seen as an epilogue to Jeremiah, but it is not a prophetic book. It is a lament, or actually five laments, like many of the psalms, and the theme is the destruction of Jerusalem in 586 BC. Nor is it said who the author is. The book was probably written shortly after 586 BC.
Lamentations thus consists of five songs, and each chapter is one song. The first four chapters are so-called “acrostic”, i.e., each verse (every 3rd verse in chapter 3) begins with a letter of the Hebrew alphabet, as Psalm 119 does. In English, it would then be that the first letter in v. 1 is A, the first letter in v. 2 is B, the first letter in v. 3 is C, etc. Consequently, this is probably not something that was written in a hurry but something that the author has spent a lot of time on.
There is some interchange of pronouns in these songs, and it can be good to know who or what is being talked about in each chapter. In chapter 1, it is Jerusalem who is both “she” in the first half and “I” in the second half. She (Jerusalem) knows that it was God who was behind the destruction. It was because of the people’s sin that it happened (1:5, 8, 18). Consequently, God was just when he judged them (v. 18).
In chapter 2, it is God who is “he” in the first half before it changes again to an “I” perspective. But now “I” is a 1st person narrator speaking to Jerusalem and urging them to pour out their hearts to God. In the last verses, Jerusalem does just this, and thus it becomes Jerusalem that is “I”. This song justifies God’s wrath, but Jerusalem is encouraged to pray to God.
In chapter 3, “I” is a “man who has seen affliction by the rod of the Lord’s wrath” (v. 1), i.e., someone who has experienced what Jerusalem is now experiencing as a result of God’s judgment. “He” again refers to God. Here in vv. 22-23, we find the most famous verses from Lamentations, and perhaps also the most important: “Because of the Lord’s great love we are not consumed, for his compassions never fail. They are new every morning; great is your faithfulness.” “I” encourage the people to seek God and put their hope in Him. What has happened should make them repent (v. 40).
In chapter 4, “we” are the people who now admit their sin. It is the same in chapter 5, where they cry out to God and place their future in His hands. Here in chapter 5, they do what chapter 3 encouraged, and there is thus a progression in the book up to this point.
Do we find Jesus in Lamentations? It is not difficult if we see this book as an epilogue to Jeremiah because we find a lot of Jesus in Jeremiah. But we can also say that the destruction of Jerusalem, which the Lamentations describe, happened so that the Messiah could come. The people had to be “cleansed” through this judgment to become more faithful. So even if Jesus is not so visible here, it is still all about him.