Take 2 or 3 baths with him, that should trigger the first option
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.
I finally found her. I'm not sure what allowed me to but here's what I did. I went back to a save before I got the quest, got my sexual interest to 100, and went to the monastery to be able to have sex with animals. After I did that I went to the lake a chose the option "Walk near the lake."
Edit: Also go at night