The Lore analysis hasn't included the Sharlayan Theory.

Essentially, given that Sharlayan has been characterized as the most advanced magical nation in Eorzea to the point the Garleans knew to fear them (Minfilia's words), and that we've seen examples of both Mhachi and Amdapori disciplines at work in the Sharlayan ruins (bound voidsent guardians in the Great Gubal Library, for example), as well as feats of magic from Sharlayan characters which broaches these fields (Y'shtola using a very White Magic looking spell fighting off Goblins in the Maker's Quarter during the MSQ), there is enough evidence to speculate that Sharlayan either discovered and revived the old arts of White and Black Magic in secret, or that Sharlayan was founded by White and Black Mages who survived the War of the Magi. A popular theory on that note is that the nation was founded by dissidents who fled the continent to study magic in peace, together, and that this is why Sharlayan is very set on not interfering in the course of history, but instead chronicling it.

The Red Mage outfit also bears strong resemblance to Sharlayan styles and themes, if you compare it to the dungeon gear from the Great Gubal Library, Shire Gear from Idyllshire, and the newer outfits of the Archons like Y'shtola, Alphinaud, and Alisae. The Magicked Crystal Medium will be the second weapon in the series that has a floating component, with the other weapon belonging to Astrologians, who also hail from Sharlayan.

A lot of players have also drawn parallels between Alisae's combat style and powers in 3.4 and similarities to Red Mage.