"White savior" is a term referring to American imperialism and the systemic erasure of indigenous culture, which had been deemed as savage and sinful by the American people. There is a faction in Final Fantasy XIV that engaged in this behavior all throughout the game's story—it's Garlemald. Hell, Gaius's signature scene is one long "Kill the Indian, Save the Man" speech.

Lyse is not a "white savior". She is white-skinned and heroic. That is not the same thing.