Lunala is based on the Minyades, three sisters who were turned into bats because they refused to honor the god Dionysus (some versions say only one of them was turned into a bat). All three went mad and continuously avoided the light of the sun after that.
I didn't know much about the Minyades before today, but it seems that when they were turned into bats they were haunted by phantom beasts. The same passage also mentions they haunted houses, though if that's the literal interpretation or not is beyond me (info found
here).
Solgaleo is based on the Nemean lion. This was a lion that could not be hurt by any sort of attack, as its fur was harder than steel. Its claws were also sharper than any weapons the mortals had, as well as their armor. The lion was eventually killed by Heracles.
Their secondary typing makes sense in light of the Greek mythological stories they are based on.