Art Scroll siddur (Ashkenaz / Zichron Re'uven) implies that there should be a piyut before *Unetaneh Tokef* (It doesn't explain why this is needed, though). On the first day, there are already several piyutim there. However, on the second day, there is nothing between Avot and *Unetaneh Tokef*. Thus, some minhagim, move *Lekel Orech Din* to Musaph.