The Robinson family plays a pivotal role in the popular soap and Dennis is the only current cast member to appear in the first episode and remain on the show (although he did take a 13-year break in the 1990s).
June Lockhart played many famous mothers throughout her career including the first Ruth Martin (the mother of little Timmy) on Lassie as well as Dr. Maureen Robinson on the 60s cult hit Lost in Space.
Guy Williams, who starred as Dr. John Robinson, 'astrophysicist', was something of a heart-throb, having appeared in two movies and a TV series as Zorro, swashbuckling masked Robin-Hood-of-the-West.
Lost is Space was clearly meant to capitalize on that popularity, by setting a resourceful family (also named Robinson) adrift in space in order to make a home as best they could.
To set the series in its time, it's important to note that in 1960, Disney had a huge hit with its movie Swiss Family Robinson, based on the 1812 Wyss novel of the same name.