I've basically followed this and I still have not run into Elyana. I even started a new save file and fresh out the game, I encountered the man in the forest who invites you to take a bath, did some repetitions of that. Still did not help.
I alternated pressing the Explore button at the lake and the option to walk around in the early morning and I did this for about 10 in game days, still did not run into Elyana. At this point, I'm starting to think it's a bug or something.