To add, your CDC card is fine for entry to Luxembourg, but to go to restaurants, the Xmas market, etc, in Luxembourg, you will need to show a EUDCC equivalent certificate that passes the Covidcheck scan. You do not need one to use public transport or go to supermarkets at the moment.

In practice, it is unlikely that you will be inspected whilst crossing the border by train and even less likely if by car, but it is not unheard of. So if you really want to respect the rules in place, you should get a predeparture test in Luxembourg, as well as a day1 test in Belgium. Covid rates are currently quite high in Benelux, so it will also give you peace of mind. There is no requirement for the rules to make sense, they are what they are.