Klingons, Romulans and blue-skinned Andorians roamed the corridors of a Las Vegas casino recently during the nation’s largest annual Star Trek convention. Other fans were dressed up as Captain Kirk, Mr. Spock and characters who appeared more fleetingly in the franchise’s six TV series and 13 movies. The most obscure reference to the Star Trek universe came from a young woman wearing a vintage dress and red curls piled on her head: a Lucille Ball costume.

The star of “I Love Lucy” played a key role in launching one of the...