"Although fundamentally unrelated to the Western sense of "goth""
This is remarkably untrue. If anything, Gothic Lolita is only one very tiny part of "Goth" in the Western sense. Gothic Lolita is part of the Western movement, not apart from it. Just because the "West" has lots of stereotypes of depression and Rivetheads with "Goth", doesn't mean that by being more Neo-Victorian than these stereotypes, it unrelated to Goth. All of Lolita is related to Goth.
And a lot of these so called "not related to Goth" Lolita/Gothic Lolita bands, make Neoclassical Darkwave. A part of the Goth subculture. Malice Mizer, make Goth music. To say that Gothic Lolita is fundamentally unrelated to the Western sense of Goth, is to completely misunderstand the Western sense of Goth. And it's sad to see people assert Japan is doing something different and unique when they do something that's only being a part of something else. In this case, they're just being a part of something Western. Gothic Lolitas aren't Japan being "uniquely Western" or having a unique take on Western culture, they're just happening to be a part of the Western Goth movement.