This is slightly outside the range for the Silver Age, as it appeared in the March 1951 issue of Action Comics, but it's such a surprising story that I couldn't resist commenting. The story is entitled, Miss Robinson Crusoe, and the premise is summed up rather well here:
Of course, Clark looks a little startled there because he realizes it's unfair for him to compete against Lois in a Survivor-type contest because he doesn't need to eat. So he decides to secretly even things up as Superman. Lois spots him changing identities, but because she's getting ill she becomes convinced (with a little trickery from Clark) that she was hallucinating.