Lucifer's wings were Lucifer Morningstar's angelic wings. Lucifer had Maze cut the wings off, and he later destroyed them.
History
Lucifer retained his wings, even after his fall from grace. However, when he and Maze abandoned Hell, they arrived at a beach in Los Angeles, where Lucifer expressed his hatred towards God by having Maze cut off his wings.
Lucifer put the wings in a secret compartment in his container. In "Favorite Son", the container was stolen by Renny under unknown circumstances. Lucifer retrieved the container, but, unfortunately, he did not find the wings where they were supposed to be.
In "Wingman", Lucifer discovered the wings Carmen Grant put out for auction were fake, and that Grant kept the real ones. Lucifer rushed to Grant's house and took them.
Lucifer later burnt them in front of Amenadiel, as the angel was the one that had tipped Grant off to steal the wings, in an attempt to encourage him to go back to Hell.
Unknown to Lucifer, Maze kept a small feather belonging to his wings. When Amenadiel was dying from a fatal wound with no hope of survival, Maze revealed the feather to him and used it to heal the wound.