(written from a Production point of view)
Lucille "Lucy" Désirée Ball (6 August 1911 – 29 April 1989; age 77) was an actress best known for her titular role on I Love Lucy. During the mid-1960s, she was the owner and chief executive of Desilu Studios, and as such, responsible for approving the initial production of Star Trek: The Original Series. Her affinity for Gene Roddenberry and favor of the general goals of the series have been cited as reasons the studio persisted with Star Trek after NBC rejected the original pilot, "The Cage". wbm
Most crucially, and contrary to popular belief, it had been Ball who had saved Star Trek from cancellation for the very first time. In February 1966, her small studio found itself unexpectedly confronted with the production of three expensive television properties, all brought in by Oscar Katz and Herb Solow (who were specifically hired to do so, in order to safeguard the future existence of the ailing studio), where there had only been one before, her own I Love Lucy show. Under advisement were Star Trek, the action series Mission Impossible and the western series The Long Hunt of April Savage (also produced by Roddenberry between the first and second Star Trek pilots), and the conservative board of directors feared, not unjustified, that the studio would financially overstretch itself. Vigorously defended by Solow, who firmly believed in the show, and despite the fact that Star Trek was already picked up by NBC after the second pilot, "Where No Man Has Gone Before", had been produced, virtually the entire board (including her second husband Gary Morton and her brother Fred, but save for executive Bernard Weitzman) unanimously voted to cancel Star Trek. Katz was also a board member, but was not present as he was already on his way out. Yet, as Chairwoman of the Board, Ball had the power to override her board, and this she did with a mere nod of her head towards Solow. "That was all Star Trek needed," as author Marc Cushman had succinctly put it, "A nod of Lucille Ball." (These Are the Voyages: TOS Season One, 1st ed, pp. 32, 94) One of the other nay-sayers on the board, studio accountant Edwin "Ed" Holly, later conceded, "If it were not for Lucy, there would be no 'Star Trek' today."  Ironically, the fears of the board were somewhat allayed when ABC canceled April Savage, before production of the regular series was slated to start.
Though overruling her board, Ball was not insensitive to their concerns as she had already demonstrated earlier, when the second pilot struggled to finish shooting on 28 July 1965, in a, for her so typical, plucky way. Keeling over with fatigue, Director James Goldstone, Producer Robert Justman and Solow had the stage cleared for another shoot, when they noticed another broom on the stage. It was Ball, who declared to Goldstone while sweeping, "What do I have to do to get you to finish?", and to Justman and Solow, "What I won't do to get the wrap party started!" (Inside Star Trek: The Real Story, 1997, p. 85)
Ball founded Desilu with her husband, Desi Arnaz in 1950. After the couple divorced in 1960, Lucy bought out Desi's interest and ownership of the studio. Soon after, she married comedian Gary Morton, who became her new business partner as Co-chairman of the Board in running Desilu, handling the studio's business and financial affairs. (Inside Star Trek: The Real Story, 1997, pp. 3-5)
During the 2006 induction of William Shatner into the Television Academy Hall of Fame, Ball's daughter, Lucie Arnaz (wife of Star Trek V: The Final Frontier actor Laurence Luckinbill), reconfirmed her mother's involvement in Star Trek's earliest days, albeit in more flowery terms. At one point, Ball's own studio chiefs said, "And the two most expensive shows are Mission: Impossible and Star Trek, [so] they have to go.' She used to always listen to everything the dyed-print suits said. But she said, 'No, I like 'em!' And they said, 'They cost too much!' And she said, 'But I like 'em!' So they left them!" wbm