Place a rack in the upper third of your oven and preheat to 450°F. Coat a 9x13-inch baking dish with nonstick spray. Pat the halibut dry and place in the dish.
In a small bowl, combine 1 tablespoon oil, 3/4 teaspoon salt, and the paprika and cayenne. Brush over the top of the fish.
Lay 1 spring of rosemary on top of each fillet, then top each with several lemon slices. Drizzle with the remaining 1/2 tablespoon oil and sprinkle with flaky salt.
Bake until the halibut reaches 145°F on an instant read thermometer, about 15 minutes (check it at 10 minutes to gauge progress so you don't overcook it). It should be opaque and flake easily with a fork. Serve immediately, with a pinch of additional salt to taste.
Notes
TO STORE: Store leftover baked halibut in an airtight container in the refrigerator for up to 2 days.
TO REHEAT: Warm gently in a low oven or enjoy cold, flaked over salads to avoid drying it out.