Lex Luthor isn't exactly proud of his alternate-universe son, Alexander Luthor Jr. Not only did he disrespect his father's legacy by starting out as a good guy, when he did switch sides he attempted to start a supervillain boy band behind his dad's back.
During 2006's Infinite Crisis event, Luthor Jr's Society of Villains proved no match for DC Comics' mightiest heroes, and after Superman and co. have defeated them, it falls to the Joker and Lex Senior to deal with their ringleader.
The evil duo find Alexander hiding in a dingy alleyway. Supes' arch nemesis gives him a dressing down and tells him that underestimating his dad was his biggest error, along with excluding the Clown Prince from his bad guy gang.
Moments later, the Joker melts his face using his acid-shooting lapel flower and finishes him off with a bullet to the head, laughing his ass off the entire time.