Warning! The following contains spoilers for the Superman & Lois series premiere. Read at your own risk!
Superman & Lois dropped a big bombshell at the end of its premiere, and for those who keep up with the Arrowverse, theories were already spinning about who Captain Luthor is right after the episode. I was all but certain that The CW series had just introduced its second Lex Luthor from another world, though upon further review, I'm not so sure.
At the surface, it completely tracks that Captain Luthor is the displaced vengeful Lex Luthor of a destroyed world. Captain Luthor knew the extensive history of Superman, his weaknesses, the perfect way to fight him, and he appears smart enough to develop technology to take the hero on. Plus, we know that "Crisis On Infinite Earths" destroyed a lot of previously existing worlds in the Arrowverse and even merged some together. Two Lex Luthors can exist, especially if one of them has already stated he was an improbable survivor of his destroyed homeworld.
It should be noted, however, that there's another character in the DC Comics telling of "Crisis On Infinite Earths" who fits the description of Captain Luthor really well. That character would be Alexander Luthor Jr., the son of an alternate Earth's Lex Luthor and Lois Lane. In the comics, Alexander lived in a world where his father battled the Crime Syndicate (the evil version of the Justice League) and was generally regarded as a hero.
If one were to take what we heard in Superman & Lois about Captain Luthor and compare it with the basic comic details of Alexander Luthor Jr., then it would track why he'd both be so knowledgeable and have a vendetta against Superman. Superman may not be responsible for the destruction of Captain Luthor's world, but that doesn't mean a character with that upbringing wouldn't believe he was somehow involved all the same.
And while two Lex Luthors would present an intriguing dynamic in the Arrowverse at large, it's hard to deny how much more interesting Captain Luthor is to the story if he's Alexander Luthor Jr. For example, he may be battling a Superman that is married to the same woman he called mother on his homeworld, Lois Lane. Seeing her would almost surely create some mixed feelings about what he's doing if I know my Arrowverse tropes as well as I think I do.
Of course, just because the show may be bringing in a character from DC Comics we've never seen before in the Arrowverse doesn't mean all we know in the comics is valid in Superman & Lois. Even if Captain Luthor does turn out to be Alexander Luthor Jr., the Arrowverse has had no qualms in the past about tweaking character origins to fit the narrative of their stories better. And I'm still not completely ruling out Captain Luthor as an entirely new displaced Lex Luthor of another world, though it's definitely worth noting there are slightly more exciting options for the character.
So, how would Superman & Lois tease that Captain Luthor is actually Alexander? The most obvious tease to me would be him tailing off an attack on Superman after seeing Lois or some reveal that he has superpowers beyond the intellect to create that fancy super suit. The Alexander Luthor Jr. of DC Comics gained the ability to control matter after surviving his Earth's destruction, which he could use to create energy blasts and create portals. Again, the Arrowverse can play fast and loose with characters, so there's no guarantee the character can do anything like that, but if Captain Luthor does, that's a dead giveaway in my eyes.