Lena Prima, the singing daughter of New Orleans and Las Vegas music star Louis Prima, is so obviously his musical child. You hear it in her warm and playful alto voice. You see it in the delight she expresses on stage. She’s a natural.

“Being on stage always felt natural,” Prima said during an interview over cheese, crackers and soft drinks at the hospitable home of the president of her fan club, Jack Porobil, and Cathy...