Some time ago I was looking for a free audio course for Luxembourgish, to listen while commuting to work, but could not find anything. Later I tried again, and found it – a free version of a more complete course from Anne Beffort, which I found useful for very beginners as well as more advanced learners.
There are three parts that you can enjoy.
You can find a couple of courses on Youtube, it includes two levels of her "Easy Luxembourgish" course, and as well as many independent videos on different topics (like common pronunciation mistakes, separable verbs, or 10 expressions with "maachen")
The Easy Luxembourgish course is also available as a podcast on iTunes, you can easily search it by name "Luxembourgish with Anne" and "Easy Luxembourgish".
You can also listen it through third party players, e.g. player.fm.
On the official site you will find short weekly lessons that can help to clarify separate topics topics (for example: Imperfect vs Perfect tense, How to say "ago", "since", "for"). The access is limited using cookies to two articles for free though... Anyway, the videos with the corresponding content are still available on YouTube.