Fact of the matter is I don't think anyone would be calling Lyse a white savior if her character was dark skinned. There is nothing in the character herself that makes her a white savior nor does her white skin ever play any role in the story. I guess someone could argue that she is then a "foreign" savior, but that's also bellied by the fact that she is literally Ala Mhigan by birth and was a child refugee. So just because she didn't grow up under imperial rule, her care for her homeland is de facto problematic or suspect?
Its not like the Ala Mhigans treated her like Paul Atriedes or something. Now that's a literal white savior, though I understand intentionally so.