Bob Cummings is clearly wearing shorts or swimming trunks in several of the shots in the bathtub.
When Lucy and Ethel dress as Geisha girls to get in so they can talk to Bob Cummings, the house manager catches them outside the dining room. She scolds the girls for being late, and tells them to get to work, but speaks to them in English. At a Tokyo Geisha house, logically she would have spoken to her employees in Japanese. (The show's writers could have used subtitles, as they did in Lucy's Italian Movie (1956) when Lucy went to Turo, outside Rome, to stomp grapes into wine.)