Many Luxembourger settlers eventually moved from the Iowa border to the Midwest. Land grants were a major draw, but so to was an expanding American industry - the railroads. Between the end of the Civil War and the mid-1880s, American railroads built new tracks across the Midwest and West. Immigrants could find work building tracks, see land, and eventually find a new place to settle their families.
The Great Northern Railroad was among these employers. The Great Northern Railroad bought and built railroads across Minnesota and the Dakotas. They then expanded further west, building as they went. Along the way, they provided a variety of immigrants with jobs.
So how do you find out if your ancestor worked for the Great Northern or another record? Your best bet is probably a census record. There's the 1880 census. In the Dakotas, there were also territorial census enumerations in 1885 and 1895. If you're willing, you can also explore the archives of Great Northern history organizations. The Great Northern Historical Society and the Great Northern Archive both have websites, though they seem focused on the railroad instead of its employees. Do some additional searches, and you will find websites, message boards, and much more. Good luck!