I just checked out a few artifacts i got and they have the Offering icon, but i cant find any guides or other places to offer artifacts. I assumed it was for a Lake Temple offering bundle but I guess not?
#Artifact lake temple offerings?
celest mural
wise elk
It's part of the S-rank questline. You'll need to get town rank A, then go through two cutscenes where the town is rewarded with rank A, and where the Mayor says we need to get to town rank S, and go to the lake after both cutscenes are fulfilled.