As for the mythology that Solgaleo is based on...

It appears to be alchemical.

Quote Originally Posted by Pokemon.com
Since ancient times, Solgaleo has been honored as an emissary of the sun. It is referred to with reverence as “the beast that devours the sun.” Solgaleo's body holds a vast amount of energy, and it shines with light when it's active. It has a flowing mane with a remarkable resemblance to the sun. Its signature move is Sunsteel Strike, an attack that charges at an opponent with the force of a meteor, disregarding the target’s Ability.

Solgaleo’s Ability is Full Metal Body, a new Ability that no previous Pokémon has had. With the Full Metal Body Ability, a Pokémon’s stats will not be lowered by the effects of an opponent’s moves or Ability.
"The lion that devours the sun" is an alchemical term and symbol referencing the purification of metals.

It's also a decently important plot point in Fullmetal Alchemist Brotherhood.
xerxian_alchemy_circle_by_icegoddess2010-d550pt8.jpg
So I don't think it's a coincidence that it's Ability is "Full Metal Body".