You meet her through investigating in your flat, in person. Its weird now but that is how you meet Emma. It wont happen on its own unlike how Pixie suggests
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There must be something you havent accomplished. What i can tell you is i progressed the artifact till after searching in the church for it. With Lily, i have worked several dozen times at the bar, you need to control her at least 2x before you're done with her. You should see a beefy guy the second time, that's how you know you've done it. You also need to work on the farm a little bit for strength check later with Lily. Progressing with Lily, Chastity, Annie, and Kana, you then should be able to meet Emma through investigation. I can't say what you havent done, but I can say it's not broken