I don't think they did, but as far as I know, the Melusine was only a legend told by the House so they could be seen as a descendants of a divine origin - According to the legend (which was written in 1393 by Jean d'Arras), the knight Raymondin and a beautiful princess Melusine started the lineage of the Luxembourgs - Which we now know is a lie.
What is weird is that Melusine was often pictured with a fish tail, but there were also interpretations of a Melusine being a half-dragon or a snake.
What is weird is that Melusine was often pictured with a fish tail, but there were also interpretations of a Melusine being a half-dragon or a snake.