Born in 1791, in Yorkshire, England, Anne Lister was a globe-trotting lesbian who dressed all in black. Her neighbors called her Gentleman Jack; in private, she was Fred. The eldest daughter of a posh family, Lister was a rarity, a female landowner, whose inherited property gave her the freedom to live as she pleased—which she did, studying anatomy, going mountaineering, and even marrying a woman, in a church. She kept a diary, too: four million words, with a subset written in a secret “crypthand.” When that code was cracked (the diaries having been found, then hidden again, by a closeted gay descendant), it turned out to be a detailed account of her seductions. An orgasm was a “kiss,” sex with a woman was “going to Italy.”

It’s no wonder that Sally Wainwright, the British showrunner behind the bleak, indelible drama “Happy Valley” and the charming “Last Tango in Halifax”—a specialist in female iconoclasts—has long wanted to tell Lister’s story. Lister was a gender-disrupting trailblazer, who recorded experiences that society refused to admit existed. (Male homosexuality was outlawed; the female version was unimaginable.) The resulting series, “Gentleman Jack,” on HBO, co-produced by the BBC, is an imperfect but enjoyable production, driven mainly by the satisfying brass of its heroine, played by Suranne Jones. When the show begins, Lister’s heart has been broken by yet another soul mate who, out of pragmatism, has married a man. On the rebound, back at “shabby little Shibden,” her family estate, Lister stumbles on a fresh romantic opportunity, one her own aunt points out: Ann Walker (Sophie Rundle), a young heiress, has moved nearby. Walker’s family frets about fortune hunters, but they don’t perceive Lister as a threat—and so, tipping her top hat, Lister decides that she will make Walker her wife.

The first five episodes document this seduction, which is a bit of a gimme, since, as it turns out, Walker has had a crush on Lister since she was nineteen, when the two had a brief interaction. There’s a dizzy charm to the sequences in which Lister woos Walker, touching her hand, planting innuendos, and then playing innocent, as if she were enacting some retro variation on the psycholinguistic programming of the pickup book “The Game.” Lister is absurdly self-assured, whether she’s shooting a horse or negotiating for coal mines, and in all-female spaces she’s viewed as a refreshing novelty, blunt and worldly. In one scene, she tells Walker, “I dissected a baby once. In Paris.” Then she launches into a lovely, earnest aria about her fascination with the body, the power of the brain, the miracle of life—and still manages to land on a whispery come-on, about how falling in love, too, is part of nature. “Isn’t every moment an inexplicable delight?” she purrs, gazing into the eyes of a dazzled Walker. “Packed with potential.”

Lister may be a historical figure, but as a TV character she follows in the tradition of fan-favorite Casanovas, among them Shane and Papi, on “The L Word,” and Nicky and Big Boo, on “Orange Is the New Black.” She’s as much a player as a romantic. If she were a man, she’d be a bounder. Like the movie “The Favourite,” “Gentleman Jack” is fascinated not merely by the oppression but also by the power of the closet, which transforms even sincere lovers into spies. As one of Lister’s exes, Marianna, tells her, in half-gripe, half-admiration, Lister is capable of “persuading everyone that black is white, or pink, or whatever color you choose it to be.” The problem is that Lister wants more: to live her secret life in public.

Rundle, as the high femme to Jones’s stone butch, gives an entertainingly arch performance: her head cocked like a blond bird, she’s a fragile, melancholic figure, in need of protection, which everyone offers up. When, a few episodes in, Walker turns out to be more complicated than her older beau understands, the story deepens a bit: the question of who is powerful, and who is vulnerable, shifts. The rest of the series is more ordinary, full of sniping at dinner parties and a few too many scenes involving coal-mine negotiations. Minor characters—from Walker’s resentful sister to the gossipy staff—are comic types or not too deeply drawn. And although the series is broken up by theatrical touches—including moments when Lister glances into the camera to make asides, a technique that seems intended to evoke the experience of reading her diaries—they never quite gel, so that, five episodes in, the show feels choppy rather than immersive.

What does work is the contrast between scenes of intimacy and the masks that women wear in public. Early on, Lister lounges in bed with Marianna, and they spar, like adults, in rare postcoital ease. Marianna is satisfied with occasional hookups, which are tolerated by her husband. She argues that Lister should marry, too. But Lister finds this plan intolerable, and she has bigger ideas. “I thoroughly intend to live with someone I love,” she says. “I thoroughly intend to spend my evening hour with someone who loves me.” It’s a touching vision: the cynical Casanova is secretly an idealist, heroic in her refusal to be anyone but herself.

“Killing Eve” is a different sort of homoerotic candy, a tart, twisty thriller that was a sensation in its first season. Co-created by Phoebe Waller-Bridge, the genius behind “Fleabag” (whose second season débuts in May), it features two wildly watchable performances: those of Sandra Oh, as the workaholic intelligence officer Eve, and Jodie Comer, as the girlish sociopath Villanelle, each the object of the other’s obsession. Generally, I prefer the plots of thrillers to make sense, and, in the first season, this one sometimes didn’t: toward the end, I had to stamp my logic-brain out like a snake just to enjoy the show. I gradually began to understand that, for the purpose of “Killing Eve” fanhood, details don’t matter. Style does. The series works best not as a literal thriller but as a staging ground for female anger, in scenes that, as on “Gentleman Jack,” are about the cathartic thrill of getting away with it, in a world in which everyone is dumb enough to see you as a helpless little girl.

The second season—with a new showrunner, Emerald Fennell—begins just after the first season’s finale, which featured Eve and Villanelle going to bed and confessing their love, and then Eve stabbing Villanelle in the gut. In the chaotic aftermath, Villanelle gets to a hospital, where she does what she always does: exploits society’s misogyny by imitating a victim of it, using her pretty-white-girl-ness (and multiple accents) to attract sympathy. She pulls this act again once she’s out, pretending to escape an abusive stepfather; and then again, playing the daughterly underling, to assassinate a political target. The idea that undergirds the show is a potent one, that femininity is itself a sort of sociopathy, whose performance, if you truly nail it, might be the source of ultimate power.

For all the series’ twists and turns—there’s a secret assassin organization, in cahoots with a secret spy organization, or something—its primal pleasure is always in watching Eve and Villanelle obsess over each other, like Hannibal Lecter and Will Graham, in their day. The two women Google and stalk each other; they judge and admire each other’s clothes. Villanelle leaves apples at her crimes, for Eve to notice. She passes her a lipstick, which contains a tiny dagger.