Trim the tops of the fennel bulb. Cut lengthwise into quarters. Trim the core. Using a mandolin, shave the fennel into very thin slices. Place the shaved fennel in a large bowl of ice water for 5 to 10 minutes, while you prepare the rest of the ingredients. This step will add a lovely crispness.
Trim both ends of the orange. Using a sharp paring knife and edges of the orange as a guide, cut off the peel of the orange, removing all of the white pith. Using the knife, carefully segment the orange by slicing between the membrane and the fruit. Set the orange segments aside.
Place the lemon juice in a large salad bowl. Slowly pour in the olive oil, whisking to emulsify. Season with salt and pepper to taste.
Remove the shaved fennel from ice water. Pat dry with kitchen linens (or alternatively, carefully dry in a salad spinner). Add the shaved fennel to the salad bowl. Toss with the vinaigrette and season with additional salt and pepper as needed. Plate and top with orange segments and shaved pecorino cheese. Garnish with fennel fronds. Serve immediately.