No, it just means that the pedigree that Lyon has access for these wondrously magnificent Griffons is a line of Griffons that are near sentience. Creatures in FFXIV actually have frighteningly proficient means of controlling aether, so it's just a matter of getting one to understand what exactly you want it to do.

Examples:

Tail Screw from Karlabos from Sastasha HM. The line from BLU spells says:


"Karlabos performs Tail Screw by collecting turbulent aether in the tip of its tail, then unleashing it at once as a violent whorl that rips foes' lives from their bodies. This is notoriously difficult to imitate, due to the challenges inherent in attempting to control such a volatile aetherial vortex."

Glower from Cyclops says:

"Perhaps best known as the unsettling hallmark of the cyclops, Glower involves funneling aether through the eyes as if they were arcane circles--much like its sister spell, The Look. Its highly concentrated aether strikes foes like a levinbolt, leaving their skin singed and muscles seizing."

The Look from Dahaks says:

"Common amongst Dahaks, this technique requires using the position of one's own eyes to anchor arcane geometries in which to concentrate aether. The user then expels the aether, propelled by ill will, in the direction of his gaze--though this tends to earn him a fair bit of ire in return."

Sonic Boom from the Zu says:

"A favored technique of the Zu, who are able to perform it with a particularly vigorous flap of the wing, Sonic Boom produces a gust of wind-aspected aether so finely compressed that its lethality is oft likened unto that of a finely crafted blade."

Cactguard from Sabotender guard adds says:

"Wild sabotenders are believed to have developed this ability to channel their aether towards others as a means of protecting particularly fruitful members of their species--as survival in arid climes ever comes at a cost."

I could go on listing these interesting descriptions about how the monsters and animals of FFXIV are able to control aether in all sorts of complex, intricate, and precise ways... but I'll stop.

Point is, is that the Griffon is just a Griffon, unless SE wants to state otherwise elsewhere. Heh. Though it's funny, I hadn't seen Dawon have to give aether for like my first 10 or so runs of that place. Thought only the machina could give it up.

We also see similar mechanics in Voidark with the Plant Dog and its Tree. Typhon and Ultros in Dragon's Neck. Enkidu and Gilgamesh in Battle at the Big Keep. Now Dawon and the Mecha. It's showing off to be a technique similar to Blue Mage's Transfusion, though far less deadly for one party than that technique.