This easy trick can solve the issue with the Moth not appearing in the Library.

Guide

1. While facing the podium (where Moth is supposed to be) go to the corner in your right.

2. Save the game and then load it, you should see the Moth for 2 seconds.

3. Before the Moth disappears use Lomus really fast and catch it.

4. Now go back to the mirror without casting any spell in your way.