Yahweh has accomplished his wrath, he has poured out his fierce anger; He has kindled a fire in Zion, which has devoured the foundations of it.
It is important to note that only Jeremiah could have written this.  It is inconceivable that anyone except Jeremiah could have written  Lamentations 4:13 without naming Jeremiah as a glorious exception to the general fact there stated.  Therefore, Jeremiah is the author.