The description of Old Moonlight, transposed from the Soul of Midir reads:
A memory of an old sword found deep within Midir. This sorcery uses souls to grant form to the thought, and attack with it.
Attacks are coupled with lightwaves, and sustaining the stance before attacking increases their speed and potency.
The sword is named after moonlight, but it is slightly different than the one fashioned of the paledrake Seath. Perhaps it is rooted in an older memory, from not long after the Beginning.
There are many lore implications than can be derived from this description, namely that it suggests that Moonlight is connected to the dragons in general, rather than Seath, as well as making reference to the very beginning of the Dark Souls universe.
However, there is also a much more subtle meaning behind this description, which I believe probably served as its main source of inspiration.
According to the Dark Souls wiki, the sword model produced by this spell is an almost direct copy of the model for the Moonlight Sword found in the game King's Field 2.
King's Field 2 is the second game ever produced by FromSoft (with its predecessor King's Field obviously being the very first).
Perhaps it is rooted in an older memory, from not long after the Beginning.
It seems pretty clear that this item is a callback to KF2, a game from not long after the literal beginning of FromSoft's game-making career.
Just thought this was a cool piece of trivia worth sharing!