http://www.fuzzy2.com/marimite/20030105.html

The area and the school is a place where the author modeled the details from. The place is the Musashino area of Tokyo - an area where a lot of manga authors, anime production studios, and industry related personnel and companies reside. 

Not to make you disappointed, but there is no real "Lillian," nor a place with a soeur system. The real name of that school is "Musashino Joshi-Gakuin" (Musashino All-Girl's School). 

HP for "Musashino Joshi-Gakuin": http://www.mj-net.ed.jp/