Lois makes some big plays to try to shake Lex Luthor out of his single-minded focus on destroying her life. Spoilers follow for Superman & Lois Season 4, Episode 05, "Break the Cycle."
"Break the Cycle"
If last week's episode felt overly full and weirdly timed, this episode feels sparse by comparison, and almost intimate. Summing it up is easy: Lex's daughter agrees to talk to him while we flash back through some of Lex's history. Lois and Clark attempt to talk their way out of utter destruction at the hands of Doomsday. Too many people are finding out about the Kent Family secret.

One of the big focuses in this episode is on where Lex Luthor places his priorities. Lex is a narcissist for whom everything is either a result of his intelligence and action or an assault on him personally. Since his introduction, he's been bringing up his daughter as this incredibly personal reason why he has a vendetta against Lois Lane. How dare you separate me from my daughter, don't you understand the importance of family?
Lois persuades the daughter, now a six-month pregnant woman with a medical degree, to talk to Lex despite her misgivings. For many people with a narcissistic parent, the whole conversation between those two should ring true.
Elizabeth (played by Elizabeth Henstridge, who also directed the episode!) is incredibly patient with her father, giving him all the rope he needs to hang himself without it ever seeming manipulative. By the end of the episode, Elizabeth is once again disappointed in her father, and her father is once again blaming Superman & Lois for it. His separation from Elizabeth was never a problem for him, it was just something to add to his list of reasons why it would be acceptable for him to direct his vast wealth and intelligence toward destroying a reporter and a guy who has saved literally billions of lives. Elizabeth doesn't let him off the hook for it. She reminds him that when she was a child, she chose to stay with him and asks him to return the favor by choosing her--to show that his wish to see her over the last 17 years was more than a symptom of his hatred for Superman & Lois. In this way, this Lex Luthor is truly authentic, and something that live-action Lex Luthors often don't get to fully explore.
I still think this portrayal of him is a little weird. He looks more like a Sons of Anarchy character than anything else. When I think back through various Lex actors, I can imagine Jon Cryer being a smarmy CEO. I can imagine Jesse Eisenberg being a techbro CEO like Mark Zuckerberg. Gene Hackman was totally believable as an ambitious but sleazy real estate mogul.

Michael Cudlitz is anger incarnate. He seethes in every scene he's in, and it's hard to imagine him doing anything other than plotting against Superman. He doesn't seem to have any other ambitions beyond that. He's not trying to be president, run the world of crime, or even prove himself the moral and genetic superior of the Man of Steel. He just wants to wreck their lives because they put him in jail for the one crime he didn't commit.
While all of this is going on, the boys are tangling with two things Superman is all too used to: keeping secrets from people they care about and protecting their identities for the sake of their family.
The way Superman died, and the place where it happened mean that many more people than the Kents are used to saw evidence of his real identity and, being people with eyes and brains, made a logical conclusion. On the heels of a classmate approaching Jonathan and Jordan, Jonathan's long-distance girlfriend Candice pops into town right as Lois is asking Jonathan for help.
This storyline is a little weird. Jordan backed away from superheroics last week, and that move made sense. But this week, Lois is asking Jonathan to taxi her around to France and Metropolis and back right as his girlfriend is in town. Jonathan doesn't do anything dangerous; he just picks his mom up, hugs her for a few thousand miles, and then stands back while she does grown-up stuff.

There's no reason Jordan couldn't do this, except that the writers wanted an excuse to torment Jonathan with the whole "with great powers comes great responsibility" thing. The same thing goes with Jordan telling Candice about Jonathan's secret. The whole thing feels forced. Instead of these ideas coming out through the story, the story was written around forcing these events.
The other interesting thing that happens (that also feels a bit weird) is that Lois summons Doomsday using her dad's Superman Beeper (there's probably another name, but this is what we're calling it) in hopes of appealing to the part of Bizarro Superman that's inside the monster. This makes sense; it fits with who Lois is and what she believes herself to be capable of. But when she uses the beeper Jonathan shows up, and she seems surprised. What's more surprising is that Clark and Jordan don't show up as well. Again, it feels like they couldn't think of a way to get him there without the beeper and just ignored the obvious questions that would raise.
The Lex parts of this episode work despite my misgivings about the overall characterization of the character. Elsewhere, I appreciate what they were trying to do, but ultimately the questions raised by the other parts are tough to ignore.
