Preheat the oven: Set to 400°F (200°C).
Lightly oil a baking dish large enough to hold the fillets in a single layer.
Prep the lemon-garlic mixture: In a small bowl, combine melted butter, olive oil, minced garlic, the zest of 1 lemon, and the juice of both lemons. Stir in capers. Season with a pinch of salt and several grinds of pepper.
Season the fish: Pat tilapia dry with paper towels.
Place in the baking dish. Sprinkle both sides with salt and pepper. Add a light dusting of paprika if you like.
Add the sauce: Pour the lemon-caper mixture evenly over the fillets, making sure some garlic and capers land on each piece.
Bake: Cook for 10–12 minutes, or until the fish flakes easily with a fork and turns opaque.
Thicker fillets may need an extra 2–3 minutes.
Finish and serve: Spoon the pan sauce over the fish. Top with chopped parsley. Serve with steamed rice, roasted potatoes, or a crisp green salad.