Luthor has always been known as a cerebral threat. A madman with a mind unmatched in the Multiverse... well until he meets his mirror image of a parallel world. And just as Lex and Alexei each found in the other the potential to aspire to greater villany and creativity, by the time they finally met they already determined that the best way to best their arch-enemies was by replicating their physical might. Which they did, through machinations and mystery.
In Lex's case, it was by trading in his prison grays or business suits for a fully functional action uniform. Colorfully arrayed in purple and green, his new clothing provided a variety of weaponry to combat mano-y-mano with Superman. As for Alexei, he used more unorthodox means, by procuring the ancient Powerstone which was of unknown origin (its Earth-One twin was the Powerprism created by the Parasite), which allowed the criminal to absorb tremendous energies which he manifested in his gigantic physique. Nevertheless, each rogue learned that relying on the muscle rather than the mental would prove to be his undoing, and the Supermen outsmarted them.
Later, Lex would visit his adopted world of Lexor and obtain an ancient powersuit that provided a similar powerset to the Powerstone, although at the cost of its planet. Alexei would soon after losing his fabled jewel adopt a costumed identity as the Light while employing various gadgets, reminiscent of his counterparts first colorful costume. Hence, each Luthor used a long lost device and created his own modern day equivalent, although in the opposite order from his twin!