As revealed in Batwoman season 1, the Arrowverse's Batman killed the Joker - but did he do so under the control of the Suit of Sorrows? Batman famously operates under a strict moral code, one that forbids him from ever taking a life. From an out-of-universe perspective, a "do not kill" vow is the only way to explain why Batman never kills the various irredeemable madmen who plague Gotham. In-universe, it prevents Batman becoming the very kind of monster he's sworn to defeat.
Naturally, that means many of Batman's worst foes have pushed him to the brink of breaking his vow. In the Arrowverse, it seems he did just that. According to Luke Fox, there's a simple reason the Joker hasn't been seen for the last five years; it's because Batman finally snapped. This was clearly kept a closely-guarded secret, and Luke only told Kate the Joker had been killed by Batman as she wrestled with self-doubt after the death of Cartwright. The circumstances have yet to be disclosed; given the Arrowverse's Batman was far on in his vigilante career, it may be a twisted version of the classic "A Death in the Family" arc, in which the Joker murdered Jason Todd and tempted Batman to commit a brutal act of vengeance.
But Batwoman may have offered another important clue as to what happened. Batwoman season 1, episode 19 featured a subtle nod that revealed Azrael - a brutal vigilante who actually donned the mask of Batman for a time in the comics - exists in the Arrowverse. Azrael is mentioned on a page of Lucius Fox's old journal, which also referenced a mystical suit associated with the character; the Suit of Sorrows.
The Suit of Sorrows is a legendary armor, which enhances the strength and speed of its wearer, but corrupts anyone whose heart and soul is not pure. According to Lucius Fox's journal, Batman wore the Suit of Sorrows for a time, but experienced what Lucius described as "an aggressive behavior" when wearing it during patrols. It's likely these events happened five years ago, given Lucius says this occurred around the time of the resurrection of Ra's al Ghul in the Arrowverse; Ra's was killed in Arrow season 3, dated in 2015, and Lucius Fox himself was murdered later that year. Thus Batman was wearing the Suit of Sorrows in the same year he broke his vow, and killed the Joker.
Lucius Fox is certainly hinting at a dark time in Batman's life, as he found himself confronting his own inner darkness. Fox's journal is silent as to just how far the Dark Knight fell; did Batman kill the Joker while under the influence of the Suit of Sorrows? Alternatively, and even more disturbingly, it's possible the Suit of Sorrows had a lasting impact on the Caped Crusader's psyche, affecting his self-control and leading to the Joker's death. According to Lucius' journal, the experience with the Suit of Sorrows taught Batman a vital lesson; "that he must be ever vigilant not only in his crusade against crime, but also himself." The Arrowverse's Batman could well have learnt that lesson because he snapped, lost control, and killed the Joker at last.
