You know, as much as I liked that story as a one-off, it struck me as increasingly silly that Luthor never followed up on it as years became decades.
On the other hand, you could make a good argument that even if Lex Luthor did know, it wouldn't be particularly useful information. It's not like knowing Batman is Bruce Wayne, where you can destroy his supporting infrastructure or attack him when he's weak, like Bane did. Superman is never weak.
You blow up Clark Kent's apartment building or the Daily Planet, you just have an ashy invulnerable man floating in the sky. You kill Lois Lane, all you've done is remove any thought of restraint from the most powerful person on Earth. This assuming you could even sneak up on him in the first place, which you couldn't.
I guess you could try to destroy Clark Kent's life, but only to a pathetic degree. Like, is it very plausible that anyone is going to try to fine the Planet for paying an illegal alien, revoke a marriage license for being entered into under a false name, or commence deportation proceedings for a living god? Even if that worked, all you've accomplished is exiling Kent and Lane to the North Pole where they can devote their entire lives to fucking you up. If anything, letting Clark Kent exist is good for Luthor, since the time off Superman needs to be Clark, hold a job (however tenuously), and somehow maintain his marriage (despite being a terrible husband) at least levels the field a little bit.