Lettice as a name for girls is of Latin origin, and the name Lettice means "joy". Lettice is an alternate form of Letitia (Latin): Latin variant of the name.
I thought it was the Mr. Bugg (as in Bug) Show and she was part of the Mr. Bugg Fan Club. All of the members had cutesy garden related names like Lucy Lettuce, Rover Clover, Rita Rose and Onion Breath, just to mention a few.