Surprisingly, the Burtons approached Lucy at a party with the idea of being guest-stars on her show and the result was a very funny episode.
A script was rushed into production by longtime (but long gone) Lucy writers Bob Carroll and Madelyn Davis. They reworked a gag they had written for both I Love Lucy and The Lucy Show - Lucy gets Elizabeth Taylor's ring stuck on her finger before it has to be presented at a gala party that evening.
All wasn't happy on the set. Conflict arose early when Lucy suggested Richard Burton read his lines a bit stronger. The great Shakespearean actor responded by shouting his lines all through the dress rehearsal. He wrote in his memoirs, "I loathe Lucy!" The filming went on without a hitch, however.
That episode, the first for the 1970-71 season, was the highest rated program on any network for the premiere week and the second highest rated Lucy episode ever.