I'm stuck at this point too. I found the sand at the school, but not of locations have any options to search for Lyx. Claire has helped Emma come out of her room, and I had a morning scene with Claire and Pixie, is there something I'm missing? progressing the story seems to require talking to Lyx.
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I'm at the point where I'm locked in the city still though, and one lead is to find Lyx, the other I need her XD
You are trying to track her down in the city. First you find notebooks that lead you to the school, there you find sand, but the areas available don't have sand as far as I can tell.
As far as unlocking the city I have the West side unlocked, and I need Lyx to unlock the East side
Edit: I think I found it! I hadn't unlocked the old club yet. Hopefully that is what I was missing.