I think the difference between Jonathan/Nancy and Lucy/Maximus is that if there are any issues between Lucy and Maximus, they'll be issues that more or less make sense. Issues that I can think of off the bat include ones like:
The whole fact that Lucy never once mentioned Maximus in any conversations with Hank or the Ghoul. Compare that to Maximus having conversations about Lucy with Dane and Thaddeus. That could be oversight by the writers due to being pressed for time. Or it could be a sign of Lucy bottling things up because of how she was raised to suppress her negative thoughts. Or it could be a sign that Lucy's feelings for Max aren't as strong as his feelings for her are.
In 2x04, as Lucy and the Ghoul left the camp, she mocked and dismissed the NCR soldiers who nursed her back to health as "matching jackets". Maximus is likely going to be joining the NCR's army as he re-connects with his roots. I could see that being a point of contention between them, especially with things like:
Lucy's lack of closure with the Ghoul. Sure, the Ghoul betrayed her to her dad...but he also came back and saved her from being chipped, and then left, but not without leaving her a little gift in the form of his bootgun. And by Ella Purnell's own admission in one post-episode 5 interview, the betrayal stung so much for Lucy because by this point in time, the Ghoul has become the person she's closest to in the wastes. Which makes sense given that they'd been traveling together for at least a month if not more by the time the betrayal happened. And I can't help but think that she feels like things weren't resolved between them after the betrayal, given that he ditched her.
House likely courting Lucy as a potential employee. Given what he said to Cooper about how "everyone works for me eventually," and the fact that Cooper ditched him to go on his personal mission, House probably wants a new human asset on the ground to help him in whatever war is coming with the Enclave. Given they showed House's face briefly flicker on the monitor in the last shot as Lucy and Maximus were looking out the Lucky 38 penthouse windows, I wouldn't be surprised if he decides to recruit Lucy. House can take advantage of:
Lucy's inquisitive nature and her desire to learn more about what her dad was doing, and take advantage of the aforementioned thing about her not wanting to be a "matching jacket". He might even have the means to figure out that Lucy is someone who can be persuaded to do questionable things for a "good reason" (her massacre of the Kings ghouls shows what she's like when her inhibitions are lowered).
Those particular traits not only would be ones that House might use to convince Lucy to work for him, but they'd also be ones to create a wedge between her and Maximus. Maximus has lines he won't cross (he refuses to kill ghoul children, hence why he killed Xander), but it's hard to say what Lucy's limits are, and I don't know if Lucy knows those either.
Maximus is not exactly the inquisitive kind either. We saw this on display in Vault 4, where Birdie easily distracted him with a goodie basket and a residence he could unwind in while Lucy was busy investigating the vault to find out its lore. If Lucy wants to find answers to what her dad was up to, and "meet her makers", I could see this putting her at odds with Maximus.
What Wilzig said to Lucy in season 1 still holds relevance: "You are a vault dweller, but if you're going to survive, you need to start acting like a surface dweller. Question is, will you still want the same things when you have become a different animal altogether?" When Lucy invited Maximus to come back to Vault 33 to live with her, she was still in the mindset of a Vault Dweller. She's changed significantly since then, and so has Maximus. What they had could be best described as a "puppy love", as Maximus was the first nice person she met outside of the Vault, and seems to want most of the same things she wants. But she only really knew him for a few days before leaving him at the Observatory. What she wants in life now has changed, and so have Maximus'.
Lucy's dad worked for the Enclave. It was established in Fallout: New Vegas that the NCR dislike the Enclave enough that they treat the descendants of known Enclave members like war criminals. If Arcade Gannon joins the Remnants and fights for the NCR at Hoover Dam, he's forced to go on the run once word gets out about his origins (if the Courier sides with the NCR) or he's arrested and imprisoned (if the Courier sides with the Legion). Given this, when the NCR learns that Hank is the man who destroyed Shady Sands and kidnapped several NCR Rangers for his project AND that he's a member of the Enclave (something that'll inevitably come out if they get any soldiers down into the management Vault), it's possible that they might not be too trusting of Lucy, even though she spent season 2 pursuing him to bring him to justice. This was even foreshadowed by the Ghoul during the "matching jackets" exchange.