The longer I research, the more apparent this becomes. Because immigrants from Luxembourg were so few in number, Luxembourger-American families with the same surname tend to be related. So what does this mean for you? Chances are high that someone has already done research on your family.
You have a few ways to find it.
1) Enter the family surname + genealogy into Google.
2) Check out the Luxembourg boards on message board sites. Here's one example.
3) Visit Luxembourg American Families.