Did you do the Bridge event at night that causes The Shopkeep to appear? Do that, then a certain character will appear at night, and Lyx will appear shortly after (make sure to read your Leads after she leaves).
Claire is the person who appears. If you have Claire already then check your leads to be sure that you don't already have the Lyx lead :)
Talk to Emma in her room, and follow that storyline; it'll trigger Claire then consequently Lyx.
