Re: 1930s Superboy and the 21st Century LSH
Here's an idea:
As Superboy has adventures in the 30's, Hitler takes note. He consults a magician (pick one; I don't know the DC universe myself) who tells him that Superman will help the Allies defeat Germany. The magician devises a villainous plot to lure Superboy to his secret base. The magician freezes Superboy in a block of ice, but not before Kal-El sets the base to self-destruct. The base is destroyed and Superboy is lost.
Without Superboy to make him jealous and evil (if that's still in the continuity), Lex Luthor becomes America's greatest hero of WWII. After the war, Lex turns his supergenius toward creating the futuristic world of LSH. By 2006 we've got flying cars and the whole shmear. But old Lex, now a powerful icon, is giving in to his evil nature and taking over. The LSH cannot stop him. When they flee from his robots to the arctic, they find a young man frozen in an iceberg...