I have had that happen a number of times. And it seems to happen often with the first few fruit I harvest from a plant.
Mainly from the Hawaiian varieties like Sunrise from my experience.

I grew a papaya tree from a potted plant 2 years ago and just got my first fruit. It too was seedless and it wasn't very sweet either. Should I be able to grow sweet papayas in Orange County California?

I have seen it before with papaya but I am not sure how common it is. I can think of a some different reasons why the fruit were seedless. It is possible that the flower was pollinated but fertilization did not occur. Or sometimes auxins can be used to stimulate the flower to form a fruit without fertilization. That too will cause seedless fruit. Another possibility is that since it was the first few fruit the plant set those fruit without pollination and fertilization because there was nothing around the pollinate it and it wanted to make fruit.

Hi, My "Red Lady" papaya flowers are opening now, in the home and under artificial light. The flowers are all female. Is it possible for it to set fruits?

Thanks

Luigi

A little weird that you bumped a really old thread to ask this question.

Are you sure they are female and not hermaphadite? If they are female, and you don't have a male nearby, then no, it will not set fruit.