Mix paprika, salt, black pepper, onion powder, garlic powder, lemon pepper, and cayenne pepper together in a small bowl.

Combine olive oil and butter in a small, microwave-safe bowl; heat in microwave until butter is melted, about 1 minute. Stir to blend butter into the oil.

Brush some of the olive oil and butter mixture over both sides of each red snapper fillet. Sprinkle paprika mixture over both sides of each fillet.

Heat leftover oil and butter mixture in a skillet over medium-high heat. Fry red snapper until flesh flakes easily with a fork, 4 to 5 minutes per side.