You have to learn to say no to this, or to satisfy these requests in ways that meet her needs without actually dumping a bunch of money on it.
Like Drunk Elephant -- this is about being able to say it's what she uses. She doesn't actually "need" it and don't go out and by a $100 serum. Get something like this as gift for a special occasion (the occasion can be starting at a new school):
https://www.ulta.com/p/day-dream-kit-pimprod2035175
Tell her this is it for the year -- you are not buying full size bottle and you aren't replenishing this unless she asks for it again for Christmas/Hannukah or a birthday. So she can use small amounts if she wants to experiment, and she can tell her friends she has Drunk Elephant, whatever.
Same with Lululemon. You can get stuff on Poshmark or you can shop their "We Made Too Much Sales" to get her a couple things. If she wants specific full price items in specific colors, she needs to ask for it for a birthday or holiday and it is not a gift on top of what else she might get -- it's one of her big-ticket gifts.
Or you can say no and explain that this is not part of the family's value system to spend money on these things and if she wants them, she needs to ask grandma or save up birthday money or get a summer job or something.
You need to figure out what matters to you and then go from there. But you aren't required to spend $800 on skincare and athleisure for your teenage daughter just because some girls at school were bragging about it. If you go that route, you're screwed because it's just going to be one thing after another.