Warning: The following contains SPOILERS for the Gotham Knights premiere.The pilot episode of Gotham Knights confirms that the Batman of this reality broke his classic rule and killed The Joker. This continues a trend in recent Batman adaptations, where the Dark Knight's use of lethal force is meant to set it apart from more traditional interpretations. In the case of Gotham Knights, however, it also serves to increase the tension between two of its lead characters.
https://screenrant.com/gotham-knights-batman-rule-joker-kill/