This little tale had Superman and Luthor facing off under a red sun (thus superman didn't have his powers), so it was a bare-knuckle brawl....that ended with the two becoming separated, and Lex saving the planet's inhabitants (while convincing them Superman was evil).
Luthor was unsuccessful in finding water for the people, and goes back to fighting Superman, but throws the battle, and on their way back to Earth, convinces Superman to redirect water to save the planet's inhabitants, so that while headed back to prison, Luthor feels like a hero.
...where readers and Luthor learn that Brainiac is really a robot, uses his own genius to increase the threat of Brainiac by increasing his intelligence, and then Luthor returns to the planet where he's thought of as a hero, battling with Superman all the while!
Luthor is on the red sun planet, now named Lexor in his honor, where he spends time as their hero, the Defender (having gotten temporary super-powers), and has to stop Superman who was stealing rare crystals (which, unknown to the Lexorians, were emitting dangerous radiation).
Luthor leaves the planet with Superman to save the Lexorians, including his girlfriend, Ardora.
Wishing to read these classic tales?
...Superman #239 (June-July, 1971), the Superman in the Sixties tradepaperback of 1999, Superman: The Greatest Stories Ever Told Volume 1 tradepaperback of 2004, and in the Superman vs. Lex Luthor tradepaperback of 2006.
...Superman #245 (also known as DC 100-Page Super Spectacular #DC-7 from December-January, 1971/1972), Superman: The Greatest Stories Ever Told Volume 2 tradepaperback of 2007, and in the Superman vs. Brainiac tradepaperback of 2008.
Sadly, the story from Superman #168 hasn't been collected anywhere in America....as of yet. After all, who'd believe Luthor could be the hero?