Honestly, when I started researching my family's past, I - and many of my relatives - thought they were outliers. How many families from Luxembourg ended up in the Midwest? As it turns out, we were very wrong. We never would have discovered our mistake without the help of the Luxembourg-American Cultural Society.
I've yet to visit the Society in person, but I would highly recommend their website. Their Luxembourg-American Cultural Society genealogical links offers a list of different resources for researching Luxembourg-Americans. Some are more historical, whereas others are straight genealogy. Poke through and see what you find. I was able to pinpoint exactly why my family left. Ironically, they were the farthest thing from outliers. They were part of one of the largest out migrations from Luxembourg.