After returning to Thetima to finish the To Shell With It quest (which was very buggy, but it seems to be a known issue), when I was about to return to the island I noticed that the Isle of Storms quest text updated itself (pointing me to collect the two moon fragments) even though I had not yet entered the Moonlit Shrine area. I didn’t notice until after I returned to the Coral Pools, so I don’t know exactly when the quest advanced itself. When I did enter the Moonlit Shrine, Architect Liath was already gone even though I never talked to her.
The quest then automatically updated itself when I entered the Coral Pools, automatically checking off the “collect moon fragment” task for that area, even though I didn’t do anything. I collected the moon fragment from the Strand of Storms normally, and opened the portal to the Temple of Lagon by activating the altars, successfully completing the quest after entering the portal (starting the Lagon quest).