We discussed earlier the meeting between the two greatest geniuses of their parallel planets, now lets dissect their meticulous and maddening manipulations versus the Men of Steel. Lex Luthor learned of the existence of Earth-Two, and traveled there to meet and exchange places with his counterpart Alexei Luthor. While Lex bedeviled the original Superman, Alexie dueled with Earth-One's Superman, neither permently vanquishing their new foes. Left in the limbo between universes, Lex proved the master strategist, providing a way out of their predicament by transporting them both to Earth-Three to renew their attack on the Kryptonians.
And yet, appearences can be deceiving, for upon arriving on Earth-Three Lex was surprised with Alexei's access to advanced equipment. Turns out that Alexei had visited this Earth months prior, planting such devices as his ion tractor beam with the intent of destroying both Earths One and Two by merging them together. Why he didn't proceed with this plan, and instead resumed his personal grudge against Superman, shows how truely insane Alexei was at this point in his life. Evidently, senility had begun to creep in despite his considerable intellect (earlier in this tale, when he met Earth-One's Lois Lane he said he had met her before, when in fact it was his world's Lois whom he had known for decades). So while Alexei had formented his scheme on Earth-Three, around the same time Lex had visited Earth-S and attempted to assist Mister Mind in defeating Captain Marvel, which proved fruitless. So had this plan, as the Supermen both defeated the Luthors and prevented their adopted worlds from merging and exploding.