I have always heard that Social Democrats have never won election in LUX because everyone there is already pretty rich so there's no need.
Truth to that?
No; southern Luxembourg is very industrial (steel) and back when that was even more so, the LSAP polled the most votes on a couple of occasions (1951, 1964, 1974) though never won more seats than the CSV. Think it may have been a straightforward malapportionment issue, though don't know for sure. There was at the time also a comparatively strong (best result was 17% in 1951 and they polled double digits as recently as 1974) Communist party, which was also strongest in the south of the country.