The song refresh will only read lyrics if a song did not contain any lyrics previously. If you changed lyrics, you will need to refresh them in the lyrics editor. Here is the reason: ST3 can not determine whether the lyrics have been edited. You definitely don't want to overwrite edited lyrics while refreshing the song list.
I will add this information to the user manual.
So when editing lyrics outside of ST3, open the lyrics editor for the song and tap on the refresh button in the navigation bar. This will reload the lyrics from the file.