>>44927277>>44927351She is named after a lily because when most people think of a lily, they think of a white lily. They're a common symbol of purity, and unstained things. The entire point of her character is that she is an extremely innocent, clean, well-mannered girl.
While the Ice Type usually doesn't play this trope, it is not unheard of in fiction for snow to symbolize purity as well. To be "as pure as the driven snow", that's where Snow White gets her name. Fresh snow is one of the most brightly white things in all of nature. And the fact that snowflakes are delicate and pretty-looking, and blankets of snow are soft and make things quiet paints a feminine slant on it.
I can't think of a single other Ice Type that plays this trope, but Alolan Vulpix and Ninetales seem to be doing it intentionally. They are very calm and soothing, they aren't vengeful like vanilla Ninetales are, they're the opposite. I suspect the entire reason WHY Alolan Ninetales is a Fairy Type in the first place isn't some bullshit about "fairytales" but rather just because they were trying to hammer home the girly pureness of its design.