June Lockhart had the biggest parking space on the "20th Century-Fox" lot because she would often drive her favorite vehicle to work - a 1923 fire engine.
Irwin Allen pitched his idea for the series to CBS programmer James Aubrey, who immediately snapped it up. A few weeks later Gene Roddenberry pitched his idea for Star Trek (1966) to Aubrey, who turned him down. He felt that this show was the more commercial of the two.
Bill Mumy has said in interviews that his father/son scenes with Guy Williams are among his most favorite ever. He has also said in interviews that he's very sorry Lost In Space became the Will Robinson/Dr. Smith/Robot show, and that Williams and other cast members were basically wasted and relegated to supporting roles.
The Robinsons' robot was created by Robert Kinoshita, the same man who designed Robby the Robot for Forbidden Planet (1956). Indeed, Robbie the Robot makes a guest appearance in War of the Robots (1966).
Interestingly, the show's most famous catchphrase, "Danger, Will Robinson!" -- was actually only uttered once in the entire 83-episode series' original run. "Danger! Danger!" not followed by any particular name, is heard several times though.