The library at the University of St. Thomas has developed a wonderful resource for Luxembourg-American researchers at http://www.stthomas.edu/libraries/collections/special/research/luxamdir/iowa.html. As part of their website, they have created a list of historical societies and university libraries with collections that might be relevant for research. These lists include a description of the collection, relevant contact information for each society, the street address, a website, hours and more.
The list is not perfect. I noticed some major repositories missing. North Dakota contains only the State Historical Society and the NDSU archives, missing the Richland County Historical Society. There are no references to Jackson County, Iowa historical society and museums, an area with a large Luxembourg population.
However, if you need a starting point for your offline research... This is it!