When you go to Luxembourg on a valid Schengen visa, you'll have access to the Schengen area for all your stats, and be allowed visa-free entry from most Schengen countries as well. If you are a citizen of an EU member state with no valid visa-free entry agreement with another country, or if you've previously been denied visa-free entry from any of these countries, then you'll need a valid Schengen visa if you are traveling to Luxembourg. You should not worry about having to introduce a passport when visiting Luxembourg.