Superman & Lois is getting its start by reusing Arrowverse villains and introducing ones that come from Supergirl's stories, not Superman's. Even from the early days on Arrow, the Arrowverse has made it a habit of using other superheroes' villains in their stories. Perhaps the most notable cases in Arrow were Deathstroke and Ra's al Ghul, who are primarily recognized as Batman and Teen Titans villains. It's not like they hadn't fought the Green Arrow before, but that's not what they were known for.
Then when Supergirl premiered and later joined the Arrowverse, it repeated the same tradition by using Superman's villains. The most prominent example is Lex Luthor, whose sister Lena Luthor was already part of Supergirl's life, but not as an adversary. While the series did confirm that Superman has his own history with Lex in the Arrowverse, Supergirl still seized the opportunity to utilize Luthor while they could. He was far from the only one, though, seeing as Supergirl has also used Metallo, Parasite, and even Silver Banshee. Now, Superman & Lois has done the same thing.
In order to get the Kents to move to Smallville, one of the deciding elements was pushing Clark and Lois out of The Daily Planet; that was a result of Morgan Edge buying the media outlet and issuing layoffs as well as rewriting Lois' article. While he was changed to a Superman villain in the comics, Morgan Edge already appeared on Supergirl and had his own story arc there. Additionally, Superman & Lois episode 3 ended with a tease for Lesla-Lar, a Supergirl villain who was jealous of Kara Zor-El and wanted the world to adore her as a superhero.
It's unclear why Superman & Lois has brought in Lesla-Lar, but it could ultimately tie into the alt-universe Luthor traveling around the world looking for Kryptonite to kill Superman. In the comics, Lesla-Lar teamed up with Lex Luthor to kill Superman, but it was merely one step in her plan to ultimately replace Supergirl as Earth's Kryptonian hero. Perhaps that story will play out similarly in the Arrowverse, and her appearance on Superman & Lois is part of that master plan - but at the moment, it seems unlikely given her connection to Morgan Edge.
All of this highlights the fact that Arrowverse shows continue to use other characters' villains. It's possible part of that is because while some heroes were initially off limits to producers, their villains may not have been. And it's easier to recognize people like Ra's al Ghul and Lex Luthor than it is other B-level villains who general fans wouldn't know. The Flash doesn't have this problems since there's only one speedster series on the air, but it's certainly an issue - and tradition - for the rest of the Arrowverse. Right now, it would be derivative to use the same villains as Supergirl even if those villains were originally Superman's in the comics.