Collected here are a few of the best of the fights between these eternal foes, as well as a more than a little bit of Kryptonite, and even just a few other foes as well.
Let's dive right into the collection, and see what evil plans Luthor unleashed on the Man of Steel....
Action Comics #249
Luthor returns with a new plan, having made a formula that allows the scientist to radiate Kryptonite from his body, which forces Superman to go on the run to stay away from Luthor, eventually making a lead suit to shield himself from the rays and approach Luthor. Luthor ups the ante by turning all lead on Earth into glass using a satellite...which forces Superman to go to the moon to make another lead suit, with Luthor in pursuit...Superman destroys the satellite as Luthor destroys the new lead suit, and Superman appears to be unaffected by Luthor's Kryptonite radiation, so he takes an antidote to the formula (to allow the scientist to sneak up on the Man of Steel as he was glowing from the formula....Superman is now able to capture Luthor; having hidden how much the Kryptonite was weakening him).
Superboy gets the bright idea of going back in time to save President Abraham Lincoln from assassination at Ford Theatre....but, an adult Lex Luthor arrives back in time (escaping Superman from other battles), with Luthor incapacitating Superboy with Red Kryptonite (thinking the Boy of Steel was there to capture him). Only after Lincoln was assassinated did Luthor realize his error, heading back to his own time, as Superboy then did himself as the effects of the Red K wore off.
This story saw a team-up of Superman's most dastardly villains of the time...Luthor (who was Alexei Luthor, not Lex....who had kept his red hair, though not depicted as such in this story), the Prankster (Oswald Loomis), who used practical joke items (usually laced with Kryptonite or set to endanger others to occupy Superman), and the Toyman (Winslow Schott), who used toys (again, sometimes with Kryptonite) to menace Superman (and innocent victims around him) resulting in giving Superman the opportunity to capture three of his foes at once!
Action Comics #277
While Superman was on a space mission, Luthor escapes and heads to one of his "Luthor's Lairs" in Metropolis (his version of Superman's Fortress of Solitude, but Luthor's version has statues of his "heroes"...Attila the Hun, Genghis Khan, Captain Kidd and Al Capone). While relaxing there, Luthor comes up with a plan to rob Fort Knox of its gold, which Luthor was successful, turning Superman away with artificial Kryptonite. Problem is, Luthor finds out it wasn't Superman, but one of the Man of Steel's robots, that the scientist defeated. Dejected he didn't defeat Superman, Luthor returns the gold he grabbed, as he didn't want reminders of his failure to defeat Superman!
Luthor comes up with one of his most dastardly plans, inventing a helmet that allows him to animate stone, and he uses it to animate Kryptonite to attack Superboy, luring the Boy of Steel to an asteroid in a plan to kill his nemesis. Luthor's plan seemed to be fool-proof, as it took help from the future, specifically Lightning Lad of the Legion of Super-Heroes, to help defeat Luthor (to enable Superboy to grow up, and the future of the Legion to exist). But, Luthor wonders, if the future has a Legion of Super-Heroes...might it not also have a Legion of Super-Villains?
Action Comics #210
Reporters Clark Kent, Lois Lane and Jimmy Olsen were at the opening of a new amusement park, Superman Land....which has a motif reflecting the Man of Steel. While touring the area, Clark performs a few low key rescues, then finally appears as Superman to sign autographs. Not likely the fact that Superman is getting so much love, Luthor arrives to try to kill Superman with synthetic Kryptonite, planning to launch the Man of Steel into space, until Superman foils Luthor's plans.