Whether by accident of design, Superman 10 (May/June 1941) is the first time Luthor appears as a bald man.
The story, by Siegel and Leo Nowak, deals with an invisibility ray. Although it’s not entirely clear whether the ray makes things appear to vanish, or actually go away.
I say this because, when the machines that control the water supply in Metropolis disappear, the workers react as if they are no longer there, no just invisible. Either way, the mystery villain behind this demands a one hundred million dollar ransom.
Superman pretends to being the money, but in reality it’s just green paper. He unmasks the villain, and it’s Luthor. But a bald Luthor (though Superman recognizes him immediately). This may be a mistake by the artist, Nowak, as I mentioned in Luthor’s earlier appearance, talking to his bald assistant. On the other hand, this does make Luthor resemble the Ultra-Humanite, Superman’s first major villain.
Superman destroys the invisibility ray, but Luthor escapes in a cool looking rocket ship, returning in a couple of issues.