No, Luxembourg is not a cheap place to live. Based on their cost of living and compared to that of the United States, it has a slightly more expensive cost of living than the U.S. For example, to rent a small studio apartment in Luxembourg, it would cost in a normal area about twelve hundred dollars per month, and that is not cheap. In the United States, it would cost around eight hundred dollars a month.
Also, in the United States, this studio apartment would be found near the beach in a tourist area which usually has a higher cost of living than cities that are found inland. Therefore, Luxembourg would be an expensive place to live in. Also, certain grocery items seem to cost more too which is also why Luxembourg is not a cheap place to live.