In "Treehouse of Horror XXIX", Lisa had a fever dream and started hallucinating all kinds of weird things. One of which was Luci from Disenchantment, sitting on the ledge of a window on Dreamland Castle, and smoking a cigarette.
In "101 Mitigations", Comic Book Guy had a bunch of worthless toys and merchandise from TV shows, video games, comic books, and movies in his room. One of which was a figurine of Bean, Elfo, and Luci.
Luci looks similar to a shadow, though it is shown that he can cast a shadow of his own, which seems to mirror the direction he is facing. Like many demons, he has a spear-head tail. However, when compared to the demons released in The Princess of Darkness, which all have wings instead of limbs, Luci has arms and legs. Luci's figure has very little form or depth, and is accompanied with a large singular eye (that is shown), horns on his head, and fangs. His form often causes people to confuse him for a cat.
Luci is a twisted, mischievous little demon, who loves causing kinds of evil, that range from childish pranks to ungoldy, reprehensable crimes. His role is to guide Bean towards her destiny which he does by generally encouraging her towards mischief and leading her astray. His actions are usually subtle, sometimes seemingly trivial and often significantly advance the plot. It is unclear whether he knows precisely in what way to guide Bean, but it is clear that he expresses no personal agenda.