Ambassador
As far as members of the Justice League went, Lex always preferred to be captured by J'onn. Firstly, the JJ monogram was a nice change from the LL which seemed to be overtaking the entire world, and he appreciated the change of pace.
And then there was J'onn's truly refreshing honesty. He was an alien, and he admitted it, put it out there, never pretending to be someone's farmboy best friend.
Plus, the decency to actually be green was something Lex truly appreciated. Green and alien looking, and not big warm eyes and gentle hands and blinding smiles and dark, curly hair that begged to be touched-
That was another thing. J'onn had the decency to be bald, and Lex admired that as well. The rest of the League was either wearing cowls or letting their luxurious, wig-like manes hang and flow and it was just so pathetically showy. Wonder Woman probably used the same shampoo Lionel always had. But now Lex is imagining his father in her uniform, and there are some images too scarring to allow free rein.
So, yeah, J'onn J'onzz. Classy guy, despite the company he kept, and Lex doesn't know how he manages to keep such a cool facade in spite of the histrionics of his teammates. The burden of heroism never seemed even remotely relevant to J'onn.
Burdens- another thing which set JJ apart. His arrival on earth from his own planet was marked by hideous alien destruction of the most vile kind, with cities almost destroyed and thousands killed. Yet J'onn refused to be crippled by guilt just because his presence might be equated with the terror everyone experienced during his first days on Earth. He didn't feel like he owed a personal apology and comforting hug to all the people he might have peripherally injured, and Lex admired J'onn's ability to realize that it WASN'T EVEN REMOTELY HIS FAULT.
On the other hand, he wore a cape, which was evidence that J'onn was taking fashion advice from a man whose obsession with flannel bordered on old school Wall of Weird material. And the primary colors- what was so wrong with purple that no spandex costumes were made in that shade? Didn't they all get sick of recycling the same palette?
It's slightly possible that Lex has a concussion. He doesn't usually let his fashion critiques progess into internal temper tantrums. It'll be gone in the morning, but between his aching head and being passed from one flying body to another, he's just a little lightheaded.
"Mr. Luthor? Where is the detonator?" See, and that will show him for getting annoyed about J'onn's costume, because now he loves him more than ever. No drama and attempts to make Lex feel like he's let anyone down, no massive guilt trips and lectures that end up being more sad than stern.
On the other hand, J'onn's mother has never made Lex pie.
"Luthor," the voice calmly repeats. Lex looks up, waving his hand impatiently. "Guatemala, but I'm sure Superman found it already. He knows where to look." Shaking his head, Lex blinks. He hates being interrupted.
Oh- J'onn. J'onn is the best, and Lex wishes he could hire him in some capacity, though he isn't sure what. Role Model? Bodyguard? Mascot?
That would probably be insulting, but he doesn't mean it in a human-centric patriarchal sense at all. He just thinks having J'onn on LexCorp stationery would really make him hate budget proposals less. And a statue! In front of the towers, green and stern and keeping a polite distance, never edging under anyone's skin until they aren't sure which impulses are their own and which are borrowed for the sake of another's opinion.
Do statues have opinions? Probably about pigeons. Lex will go into the lab and create a pigeon repellent for his J'onn statue. The base of the statue will emit some substance which has no effect on humans but drives pigeons away, never to return.
They can go gather around The Daily Planet, pissing off reporters, and dammit, now Lex kind of likes pigeons because of all the petty humiliations they could visit upon the newspaper's staff. Hard to walk into a press conference looking like that, right?
"Ever posed for a statue?" he asks, thinking he should maybe stop trying to think or talk, but hey, he's a major patron of the arts. Maybe J'onn doesn't look like the classical Greek conception of a Muse, but Adonis wasn't supposed to fly, so Lex is going to gently tell the Greeks to suck it up.
"Perhaps I should take you to the hospital."
"No, I don't like doctors. They sometimes strand me on desert islands, which is frankly redundant. I'm always trapped in vehicles as they plummet into bodies of water. The river was deeper, of course..."
The air stirs with a new arrival, just like every time he gets to this part of the story. "I'll take him home, J'onn," a tired voice says, and Lex just laughs.
Liar.