Why does Demeter adore Persephone?
Demeter adores Persephone because persephone is her daughter and the official start of spring
Why does the lion represent Demeter?
Demeter has many representations, but I've never heard of the lion. My best guess is that it's because she can be quite a roaring word that begins with "B" and rhymes with "witch".
Demeter is a Goddess, an Olympian, a daughter of Kronos and Rhea. She is by no means a demigod.