Using kitchen shears, cut the top of the lobster shells lengthwise down the center. Pull apart shells slightly, and season the meat with salt and pepper.
In a small saucepan, melt the butter over medium heat. Add the minced garlic and cook until fragrant, about 1-2 minutes. Stir in lemon juice and paprika.
Brush the garlic butter mixture over the lobster meat.
Place the lobster tails on a baking sheet and bake in the preheated oven until the meat is opaque and slightly browned, about 12-15 minutes.
Serve immediately with additional garlic butter on the side for dipping.