In “Lucy and the Undercover Agent” (THE LUCY SHOW ~ November 1965) Lucy dresses up as ‘big Broadway star’ Carol Channing – even singing a few bars of “Hello, Dolly”.  Channing does not appear in the episode herself.  She was then in her second year of playing Dolly on Broadway.  Another big Broadway star, Jack Cassidy, is also in this episode.  Cassidy had just finished a run in FADE IN / FADE OUT opposite Carol Burnett.  Lucille Ball and Channing were on Broadway at the same time in 1961: Lucy in WILDCAT and Channing in a revue called SHOW GIRL.