When the event starts there is a message you could find something back at home. At that time there is a new option under the "Study". You can learn the recipe for Spectral Sirup, but it's not all you need. You still need to learn the recipe for Heat Occisia. There is a riddle, but you can also go to the Priestess and ask her about how to make it. But it works only if you learn how to make Spectral Sirup first.
There's no need to do the Lost Acolyte for it.