Lix's Cafe is a dessert/coffee shop aimed at a younger clientele.
Appearing in OVA Zoku, this is a place that Isshiki takes Hachiman on their "date". The location may be a common place for dates or students to hang out at as Sobu's student council vice president and secretary are seen leaving it together. The waiter or waitress is fine with taking photos for "couples" or "groups". This business is also a place that could potentially be featured in the student newsletter in OVA Zoku.