Luthor builds a super-suit with none of the flair of his later designs, in Superman 106 (July 1956).
But the first story in the issue, by Hamilton, Boring and Kaye, is more important in the larger scheme of things. A scientist is doing research on Superman, and his earliest activities as Superboy in Smallville. Perry White decides to help him out, ordering his staff to find the earliest Superboy deed they can.
Superman is quite suspicious about all this. The scientist has a bad reputation, years earlier he had caused a panic with a false report of an approaching meteor.
But as nothing the scientist is uncovering seems dangerous to him, Superman helps out, telling them all about his voyage to from Krypton to Earth. Superman is now able to remember this, and even his parents, though of course he had no memory of Krypton in earlier tales. From this point on, his super-memory will allow him to recall a huge amount of Kryptonian details.
On the flight, baby Superman got out and played with a comet, which wound up diverting its path. This was what the scientist was after all along. His forecast years earlier had been right, but Superbaby saved the Earth without realizing it.
Luthor’s super-suit is saved for the final story in the issue, by Coleman, Boring and Kaye.
This suit is designed to harness the energy that Superman expends. So the more Superman does, the stronger Luthor becomes. Luthor causes all sorts of emergencies, charging his suit off of Superman, before confronting him.
Superman theorizes, correctly, that the suit would also transfer his weaknesses to Luthor. He exposes himself to kryptonite, which weakens Luthor as well, enough that Superman can remove and destroy the suit.