I didn't know there would be any more posts in this forum lol
Anyway, dealing with his zoning isn't that bad. Don't listen to
@EGP Wonder_Chef haha. You can backdash his lasers on reaction. While this doesn't help you get in, you can actually hold trait and backdash on reaction to the laser and keep your trait with that. From there, you can either try to zone him back or put up probes to help you get in with your armor. He can trait as well, of course, to nullify yours. But if he does that you can kinda just lame him out if he's still trying to throw lasers until it's gone or you find an opening. Lex's trait outlasts his and iirc has faster recovery so you'll eventually get your opportunities. Superman doing this also wastes his trait for potentially better opportunities, so you might sometimes get hit but you won't take any damage regardless with the lvl 3 up.
That's my main strategy, but if you're just trying to get in normally, you need to duck the straight lasers and jump the ground laser. When you make it to about midscreen you're in j3 range and have a few more normal options to beat him out. It all comes down to getting a good understanding of the lasers' timing and his recovery.