The only reason I have photos of myself in lolita with parasols is because James and I own some as part of our overall model wardrobe. They’re not exclusively mine, nor were they purchased exclusively for us in lolita. And I only ever do use them for photoshoots anyway.
Speaking of parasols and photoshoots, here's a throwback to a shoot with my lovely James aka The Enthusiast.
My neutral side does want to point out, however, that they’re not really frivolous, no more than anything else in this fashion. They can be cute or elegant, and are always lovely so if you want to carry a parasol you carry a parasol and you’ll look great while doing it! It’s just an aspect of lolita fashion that I don’t feel much need for and probably won’t explore myself, unless I suddenly start to wear lolita a whole lot more often.