Well, because Liechtenstein is a micro-state, while Luxembourg is a small state, which is a big difference. There are 5 micro-states on the European continent, all of which are not part of the EU. These are Andorra, the mentioned Liechtenstein, Monaco, San Marino, and Vatican. read more
Historically, Luxembourg got together with Belgium and Netherlands to form Benelux (in1944), and then was one of the six founding members of the EU - back in 1951, when it was just a Coal and Steel Community (with Belgium, Netherlands, Germany, France, and Italy). read more