On I Love Lucy, she also sang in the Scottish-set dragon musical nightmare she dreamed after having seen Brigadoon or something like it in London with Ricky, and as "Sally Sweet" with Ricky as "Cuban Pete" at the Tropicana. She sang intentionally badly as gypsy lady in the operetta that she and Ethel wrote for the women's club. She also sang "Under the Bamboo Tree" with Ricky. And there's the "Sweet Adeline" episode (linking part of it) where she sang particularly badly. And "Auf Wiedersehen" (sort of). And probably some others not coming to mind.
And doesn't she sing in the Merman episode of The Lucy Show? Doesn't she demonstrate to Merman how to sing like Merman? I don't remember how much she actually sings there.