https://tr.ivisa.com/luxembourg-schengen-visa

When you travel to Luxembourg on a valid Schengen visa, you will have access to the Schengen area for all your stats, and be granted visa-free entry from all Schengen countries too. If you are a citizen of an EU member state without a legal visa-free entry arrangement with the other country, or if you've been denied visa-free entrance from one of these countries, then you are going to require a valid Schengen visa if you're traveling to Luxembourg. You should not worry about having to introduce a passport when visiting Luxembourg.