Moon Rune symbolizes Destruction & Compassion.
Destruction - Shown by its capability to decimate Ancient Armes Dynasty, Lordlake and deaths among other.
Compassion - Compassion is the response to the suffering of others that motivates a desire to help. Prince's suffering of Lyon's death, motivates him and even the Sun Rune to become a symbol of mercy that fosters life, symbolized by Lyon's revival.
And we all know, that Moonlight is just reflecting the sunlight afterall.