The following article contains spoilers from Justice League: Road to Dark Crisis #1, on sale now.
The death of the Justice League has not just rattled the DC Universe's heroes, but also its villains. In Justice League: Road to Dark Crisis (by Stephanie Phillips, Clayton Henry, Marcelo Maiolo and Josh Reed), Nocturna is shown in the middle of a heist, not for material gain, but to confirm for herself that Batman is truly dead. Not just because she enjoys their dynamic, but because Nocturna also has feelings for him.
This confirms that Nocturna is Natalia Knight, the original version of the character, who at one point had a romantic relationship with Bruce Wayne. Her story is similar to Catwoman's on and off again dynamic with Batman, but unlike Selina Kyle, Nocturna has never had the desire to redeem herself.
Early in her life of crime, Nocturna preferred to not get her hands dirty, merely suggesting thefts and burglaries, but letting others handle the actual work. Eventually, she quit being a criminal mastermind and like Selina, became intimate with the Dark Knight.
The only difference between the two is that Catwoman's innate morality eventually earned enough of Bruce's trust for him to share his secret identity with her. This was never the case with Nocturna. However, Nocturna managed to gain access to Bruce's personal life in a different way, by becoming a surrogate mother for Jason Todd. She even adopted him, prompting her to consider marrying Bruce so that Jason could have both of them in his life. The relationship was called off when Nocturna's old life came back to haunt her. An old partner she betrayed returned for revenge. This made her exit Bruce and Jason's lives and resume her life of crime.
At a glance, it's easy to see how her dynamic with Batman mirrored Catwoman's. She seems to like the fact that Batman would come after her. She enjoyed their cat and mouse games so much that her feelings evolved into something more than a mere attraction. His death seemed to have so deeply affected her that she didn't even bother finishing her heist.
This wasn't just a one-sided crush either. Batman also developed romantic feelings for Natalia as well, both in and out of costume. However, Nocturna clearly wanted more than what Batman could give her. Bruce could never truly commit to her the way he did to Selina because he knows exactly who she is. Nocturna has no interest in renouncing her criminal behavior, going against what the Dark Knight stands for. So while she may be similar to Catwoman, her lack of morals will always prevent her from meaning as much to Bruce as Selina does.