Upvote:3
There is a luggage store at Luxembourg train stain open 24/7 called nannybag.
It quotes:
You transit through Luxembourg Train Station and do not know where to leave your luggage? With Nannybag's network of hotels and stores, you can find and reserve a secured luggage storage near the Luxembourg Train Station. This service is available 24/7 from €6 for 24 hours, so, do not hesitate to make the most of your day!
You can check availablity by filling out a form here.