Why, oh why did Gotham have to take a three-month hiatus in the middle of its season? It ultimately slowed a lot of its momentum, and no character's arc suffered more than Lee Thompkins', whose anger and grief about the death of her new husband, Mario, had calcified into complete and utter disdain and hatred for Jim Gordon by the time the show returned. But when Lee injects herself with Alice Tetch's blood, it takes what should be a big moment and makes it feel a little forced. Because so much time passed since Mario was killed, it feels like, by Gotham standards, that Lee should probably be over watching her new spouse be shot by her ex-boyfriend.
It feels especially odd to have Jervis Tetch return to reminisce about the days before Mario was killed, when it seemed like Jim and Lee might reconnect, and Valerie Vale hadn't been the victim of the Mad Hatter yet. Ultimately, Lee's takeaway from that exchange is that somehow, she's at fault for Jervis infecting Mario, because she was still in love with Jim, and Jervis wanted to turn her love into hate. I know this is a borderline-absurd comic book drama, but it's still kind of a weird, victim-blaming accusation, even for a villain to make. And it's because of that advice that Lee infects herself.
As demonstrated by the return of Captain Barnes, the Alice Tetch virus is extremely deadly and contagious... unless a main character has it, probably. It's communicated when someone comes into contact with an infected person's blood, but it's been effectively weaponized by Hugo Strange and will be set off around the city unless Jim can stop the Court of Owls. And while the characters-of-the-week who were infected by the virus have become generally zombie-like, mindlessly biting and scratching people, Barnes has become an executioner stalking Gotham City's criminals. Mario, briefly, became murderous and wanted to kill Jim and Lee because he suspected she was still in love with him.
Lee also hates Jim and she has a fair amount of slow-burning aggression building up. But she's not a law-and-order type — she's a doctor and medical examiner. Perhaps her virus-infected self will become obsessed with killing Jim like everyone else. Or maybe she'll become smart enough to discover a cure and stop the Court (and Jim's extralegal pursuit of the Court) once and for all.