Rinse and drain fennel. Trim off tops and reserve enough fronds to make ¼ cup. Trim and discard root ends. Cut bulbs crosswise into thin slices and place in a wide, shallow baking dish.
Zest lemon into a small bowl. Juice lemon to obtain ¼ cup juice and set aside.
Stem and peel persimmons. Cut fruit crosswise into slices and place in a medium bowl. Add lemon juice and olive oil and let rest for 15 minutes. Drain liquid from persimmons over fennel, reserving the persimmon slices. Toss fennel with dressing and season with salt and white pepper to taste.
Arrange persimmon slices over fennel. Sprinkle with feta, reserved fennel fronds, and lemon zest. Serve immediately, or store, covered, in the refrigerator for up to half a day.