Thank you!

At 06:38 you subbed it "lily yarn bracelet", but isn't she saying "Lillian bracelet", as in the actual thing + alluding to the soon to appear Precure lol?

Same thing basically. "Lily yarn" is the specific knitted-yarn handicraft that developed in Kyoto during the Taisho era. Named from the lily flower (リリー) and yarn (ヤーン). Then later on shortened to リリアン in the Showa era, partially because it's just easier to say, and perhaps also because of a popular entertainer who went by that name at the time. So "Lillian" is just a romanization of that already-abbreviated term. Also, "Lillian bracelet" does not mean the same thing in English/Western societies. It's a very generic term that can really encompass most small handicraft-looking bracelets, and usually doesn't even need to be related to yarn at all. Companies will sell bracelets called "Lillian" for no reason, other than it's just a name of the product. It's more of a marketing term than anything concrete. That conversation was specifically about the Japanese knitted-yarn handicraft though. Either term could probably be used there, I suppose.