The last filmed episode of Lucy Meets the Mustache (1960) was the last time Lucille Ball and Desi Arnaz would work together. Immediately after filming, Lucille Ball filed for divorce. This episode - and the background drama of these 2 - had been subsequently talked about. (Edie Adams discussed in detail that during the filming - and especially whilst she was singing, Lucy's eyes were visibly red... from crying. Though Ms Adams says no one on the set discussed, or even knew exactly what was going on).
The reason of the series' name change (from I Love Lucy (1951)) was that shows' title - along with all the first several years worth of episodes - had been sold to CBS. The sale was done to give Ball and Arnaz the money needed too complete their purchase of RKO Studios, subsequently known as Desilu Studios (subsequently purchased in the late 1960's by Gulf+Western).
Near the end of the series, William Frawley and Vivian Vance were offered their own spin-off series. William Frawley was for it, but not Vivian Vance; neither got along well with another, off-camera. Vance turned it down primarily due to not wishing to continue to work with Frawley. She also felt the Mertzes as leads would not work without the Lucy (Lucille Ball) character.
When this series was still being negotiated by Desi Arnaz, with CBS, a big sticking problem in negotiations was... money (what else is new?). I Love Lucy (1951)'s sponsors (P&G and General Foods) would pull out, due to the cost, and limited number of episodes (meaning less ad time but at a higher cost). Ford Motors agreed - to promote their brand new car (the Edsel). They pulled out before the second series of episodes. Westinghouse became sponsor for the next 2 seasons, with a contract for 7 episodes (8 were produced).
The Lucy-Desi Comedy Hour (1957) never had a formal finale (which was a rare thing in those early years, anyway). Plans had been made early in 1960 for another (1961) series of episodes, and Debbie Reynolds had been signed to appear in one. No other signings were made. The regular cast were subsequently released in April, 1960, with the series' cancellation.