AN: This is slightly AU for season 10 (and completely ignores the comics). Specifically, Clark and Lois broke up rather than getting engaged - which means that Martha never gave Clark the deed to the farm, and Conner and Clark have both been living there since 10x16 "Scion."
Conner had always kind of suspected that Tess didn't actually like him all that much, ever since she handed him off to Clark at the first available opportunity. To be fair, Conner is more closely related to Clark, who is biologically his father, than Tess, who is his… aunt or something, and it probably hadn't been easy for her to deal with his emerging powers, definitely not as easy as it is for Clark. But still, if she had really liked him, she probably could have worked something out with Clark so Conner could stay with her.
So yeah, Conner had suspected that Tess didn't actually like him, but when he finds out she had left the controlling shares of LuthorCorp to him, that's when he's sure.
The thing is, the shares technically belong to Lex, since he's alive again, but Conner can't just give the shares back to him. Or rather, Clark won't let him because Lex could get up to all kinds of bad things if he had all of LuthorCorp behind him.
Lex, theoretically could sue for the shares back, but legally Lex Luthor is dead. And apparently getting yourself un-declared dead isn't easy when you have no money, all of Lex's personal effects had also been left to Tess and then to Conner, and no memory of who to blackmail.
Oliver offers to help Conner out with the whole CEO of a Fortune 500 company thing, but Conner turns him down. Oliver had always been kind of shifty-eyed about the Conner being sort of Lex's clone thing.
Conner doesn't have any idea how Tess managed to run Metropolis-based LuthorCorp while living in Smallville. Conner is having a hard time doing it and he has super-speed.
Neither Conner nor Clark feel comfortable moving into the penthouse exactly, but Conner is rich now, so he totally just rents them a two-bedroom in one of the nicer areas of Metropolis. Martha is kind of upset about them abandoning the family farm, but duh, Conner is rich now, so he just hires some farm hands to take care of the day to day stuff.
Both Clark and Martha grumble a bit about solving problems by throwing money at them, but Conner really doesn't see what the big deal is.
Bruce Wayne proposes a meeting with Conner at his home office to discuss the possibility of a partnership between LuthorCorp and Wayne Enterprises. According to the board this was virtually unheard of, so Conner accepts.
He's a little suspicious at first when "Please-Call-Me-Bruce" offers Conner the same mentorship-type deal that Oliver had. But then the butler Alfred, who makes even better chocolate chip cookies than Martha – not that Conner is ever going to tell her that – confides that "Master Bruce" has a soft spot for kids in distress or tricky situations and Tim Drake, who is totally awesome and hanging around Wayne Manor for no adequately explained reason, backs him up. So Conner figures it's probably okay, and agrees.
Bruce almost smiles.
Conner hates the name LuthorCorp. It reminds him of Lionel Luthor and makes him feel slimy. So he changes it, to KON Corp, and smiles mysteriously whenever anyone asks what the K-O-N stands for.
Really, Conner just likes sort of having his name in the company name. And the alliteration.
Conner feels bad for Lex, and not just because he's poor and amnesiac now. Lex is recognized as Lex Luthor enough for people to be mean and judgmental about it, but not enough for the normal fear and respect to kick in and counteract it, which sucks. Plus Conner wouldn't even be alive if not for Lex, so Conner kind of owes him.
That's the reason, sans the part about why Conner owes him because that could raise all kinds of questions that Conner isn't supposed to answer, and with the part where Conner stumbled across some of Lex's notes in Tess's stuff and found out Lex is a total genius, that Conner gives Lex for why he offers him the job of head of R&D. Conner is a bit worried that Lex's pride might make him say no though, so Conner does his absolute best to be charming. And it works, or maybe Lex really doesn't have anywhere else to go, because he accepts.
Conner waits until after Lex says yes to tell him one of the perks of the job is the penthouse. It's not like Conner is using it.
Clark is pretty pissed when he finds out that Conner has hired Lex, since all evidence suggests that Lex is still kind of evil. He threatens to ground Conner, until Conner points out that this way they can keep an eye on Lex.
You know for such a genius, you'd think Lex would figure out that Conner is not going to green-light any projects that are obviously traps for Superman.
Conner, or Kon-El as the Fortress insists on calling him, and Jor-El come to an agreement. Jor-El will stop trying to backdoor Clark into taking over the world by being the world's greatest superhero, and "Kon-El" will do his best to rule the weak humans with economic strength.
One of the board members finally gets around to contesting Tess's will, the will where she leaves a multinational corporation to a fourteen year old boy who, as far as the general public is concerned, has no relation to her outside of being the foster brother/son of a friend of hers. Conner isn't sure if Peterson has been biding time and collecting evidence or something, or if he's just slow, but Conner's definitely leaning toward the latter.
Clark and Conner decide that the easiest way to defuse the situation is to, with some help from Emil, have Conner take a DNA test to prove that Conner and Tess were related.
It had seemed like a good idea at the time.
Lex can't seem to decide if he's angry at Conner for keeping the truth from him, or upset that Conner would apparently rather be an orphan than have Lex for a father. Conner finds the whole thing immensely depressing, plus it makes their work relationship super awkward.
Finally Conner breaks down and tells Lex the whole sordid half-alien enhanced aged clone baby truth. Lex seems a bit mollified, but he's astonishingly quick to jump from half-alien to alien parent to Superman as Conner's other dad to Clark is Superman.
Conner is totally telling Clark that Lex secretly knew all along.
Board meetings suck. Conner sends Tim a text that they should be called BORED meetings. Tim sends one back that Conner isn't as clever as he thinks he is. Tim sucks too.
Clark, AC, and Mera take out a facility they think is making an underwater weapons system that Lex managed to sneak past Conner. It's actually working on a joint Wayne Enterprises-KON Corp project from government contract that Bruce and Conner went to a lot of effort to get. And it's not like all the inadvertent fish deaths weren't right near the top of their list of things to fix.
Conner was going to give Clark the cold shoulder, but then Bruce starts ripping the three of them a new one about interfering in things when they don't have sufficient information and taking action excessive to the perceived crime. At that point Mera jumps in, yelling about how no one respects Atlantis or the denizens of the ocean and things get scary fast.
Conner ends up giving Clark a hug instead. He seems like he needs it.
The press will not let the Conner living with a man he is (supposedly) unrelated to instead of Lex, his father, go. Theories range from Conner being a cold-hearted uncaring son, to Lex being a soulless child abuser, to Conner not believing that Lex is really Lex.
Conner eventually puts his foot down and tells Clark that he has to stay with Lex in the penthouse at least part time. Clark nods and makes reassuring noises about Conner being a young man and mature enough to make his own decisions as to which parent he wants to spend time with.
Then Clark tells Conner there's no way in hell Conner is living alone with Lex and Clark is moving into the penthouse too.
Clark and Lex can't go more than an hour without getting into a fight. This is going much smoother than Conner expected.
After they move into the penthouse, a bunch of KON Corp labs start blowing up. Conner can't prove anything, but he's 95% sure Oliver is behind it. Partially because Oliver has a track record for this kind of thing, and mostly because ever since the move, Oliver's been kind of a dick – a metaphorical dick that is, not a Tim's pseudo-older brother Dick. (At least, Conner thinks Dick is Tim's older brother; their family dynamics confuse the crap out of Conner and he's still not too clear on where the bat thing is coming from.)
Clark tries talking to Oliver about it, but it doesn't do any good. So Conner pouts at Chloe until she promises to fix it, muttering something about how tremendously uncomfortable their couch is to sleep on.
Conner's labs stop blowing up. Chloe is awesome.
One day Lex wakes up and has his memory back. They aren't sure why, but the predominant theory is that Lex's meteor healing is kicking in.
Clark and Lex's fights start including recriminations about past wrongs, and their, thankfully increasingly frequent, friendly periods start including jokes about stuff they used to do together, but other than that nothing really changes.
Conner gets his GED, finally. He would have gotten it sooner, the material was ridiculously easy, but it had been hard to find the free time. He's just glad it's over with.
Conner starts taking business classes at night school. Between the things he's learned from Bruce, Lex, and on the job, they're even more boringly easy than the GED material. Sometimes, Conner's life sucks.
Suddenly and inexplicably, Lex stops trying to push through "kill Superman" plans. That's definitely the story Conner is going with – suddenly and inexplicably – and he's not even going to think about how it's happening at about the same time Clark and Lex start sharing a bedroom and their fighting turns into… something else.
He is going to think about improving the sound-proofing on the penthouse though.
At this point it's pretty clear that someone is putting up road blocks to Lex getting himself completely and legally declared among the living. Conner offers to bribe some people, just enough to put Lex on even footing with anyone else. Lex is about to accept when Clark interjects with some platitudes about two wrongs and not making a right. It ends up devolving into a huge argument and nothing gets decided.
The next morning Clark walks into breakfast looking incredibly smug and self-satisfied and declares that they decided to do things his way. Lex comes in after him looking...
Well. Conner's not going to think about that either.
The end of the year reports come in. KON Corp has experienced a 50% growth since last year. Conner isn't sure if that's because Tess was a really bad CEO, or if Conner is just that good. Either way it's pretty awesome though.
At last, all the t's get crossed and the i's get dotted and Lex is legally alive again. When they find out Clark and Lex share a lingering congratulatory kiss that Conner so did not need to see because they're his parents and that's gross.
"Guys!" Conner protests.
They pull apart and Clark blushes. "Sorry," Lex says, but he doesn't sound sorry at all.
"So," Conner says, "did you want your company back?" Because technically it is Lex's company, even if Conner actually really likes running it and thinks it's super cool being the youngest CEO ever.
Lex appears to think it over and then smiles and ruffles Conner's hair. "No. You keep it."