Dr. Tiemeyer argues that Isaiah 40-55 was written after Lamentations.
Lena-Sofia Tiemeyer, "Lamentations in Isaiah 40-55," Great Is Thy Faithfulness?: Reading Lamentations as Sacred Scripture, edited by Robin A. Parry and Heath Thomas (Eugene, OR: Wipf and Stock Publishers, 2011), 1–9
Inner-biblical allusions are a well known phenomenon. One biblical text alludes to another earlier text and, as a result, the interpretation of both texts is modified. This chapter looks at the ways in which the author(s) of Isa 40–55 consciously made use of and interacted with the laments of Lamentations. Other types of intertextuality will not be considered. In particular, we shall explore how these later Isaianic authors furnished the laments in Lamentations, texts characterized by God’s silence, with divine answers.