really wonder if the bartender Liz have a route, she is cute.

I only found 1 scene with her and it's a part of Anna's story. idk how I got it exactly. Anna will go to the bar at some point and the scene happens after you find Anna there the third time.

She has one scene.

After starting to get intimate with Anna, she'll start to show in the bar on Tuesdays. The third interaction unlocks a scene with Anna and Liz.