There is no way to date Lamentations to a specific year. Doing so is, from a historian's point of view, unethical. Even dating Lamentations to the event is problematic. My personal opinion is that it contemporary to Jerusalem's fall. But my steely-eyed historian's approach would not let me write that it is positively so because there is no way to unfailingly prove it so.
The book is important for its content. It does not support a date.