Superman and Lex Luthor had a long feud going on...
...and, in the Silver Age, it started back when Superman was a boy (as was Lex) in the small town of Smallville...
How Luthor Met Superboy!
The story of how Luthor and Superboy met was in
Adventure Comics #271 (April, 1960), with a story by
Jerry Siegel and
Al Plastino, under a cover by
Curt Swan and
Stan Kaye. It began when young Lex saved Superboy from a Kryptonite meteor. Luthor then took him to his farm home, and showed him his Superboy rescue collection (as Lex was a big fan). In gratitude, Superboy built Luthor a laboratory, so he could conduct the scientific experiments he wanted to do. Alone, Luthor discovered a chemical way of creating life. Then, to show his gratitude for Superboy, thought to make a formula to make Superboy immune to Kryptonite. While doing that, Luthor knocked over a vile of acid, starting a fire.

Superboy came by, extinguishing the flame but destroying the protoplasmic life Luthor created, and the chemical mixture caused Luthor's hair to fall out. Luthor, consumed with rage, blamed Superboy for the loss of his experiment and his hair, and began to plot to outdo the Boy of Steel. Luthor had two inventions that were suppose to help Smallville (a solar reflector to keep the town warm all year, and fast growing seeds) but both had unexpected consequences, with Superboy stopping the problem and the town turning against Lex. Luthor then retrieved the Kryptonite meteor and tried to use it to kill Superboy, and would have, had Luthor not tempted Superboy with the Kryptonite immunity formula, which Superboy inhaled. Though the immunity was only temporary, the animosity between Luthor and Superboy would last.
The Luthor Nobody Knows!
In
Superman #292 (October, 1975), under a cover by
Bob Oksner, in a story by
Elliot Maggin,
Curt Swan and
Bob Oksner, with a thoughtful Superman, repairing an airport recently damaged during a battle with Lex Luthor and his new super suit, as Luthor had caused Superman to lose control of his muscles, so Superman himself had done much damage to the airport as he worked to defeat Luthor.
Superman reflected back on his many encounters with Luthor over the years, how even as a student before he lost his hair, Luthor was arrogant and self-absorbed, but that after losing his hair, it only got worse. Luthor's obsession cost him his friends, family and pretty much everything.
Superboy still offered to help, but Luthor only responded back with hate, which was the ultimate difference between Superman and Luthor, the different between the power of love and hate.