Preheat the oven to 350°F (175°C).
Prepare the lobster tails by cutting them lengthwise with a sharp knife, and gently pulling the meat up from the shell so it sits on top while baking. Place the tails on a baking sheet.
In a small mixing bowl, melt 4 tablespoons of butter. Stir in the minced garlic, chopped parsley, lemon juice, salt, and pepper until well combined.
Brush the garlic herb butter sauce over the lobster meat generously. Reserve a bit of the sauce for serving.
Bake the lobster tails in the preheated oven for about 15-20 minutes, or until the lobster meat is opaque and cooked through.
While the lobster tails are baking, peel and chop the potatoes into chunks. Place them in a medium saucepan, cover with cold water, and add a pinch of salt.
Bring the water to a boil and cook the potatoes for about 15 minutes, or until fork-tender. Drain the potatoes and return them to the saucepan.
Add 4 tablespoons of butter and ¼ cup of milk to the potatoes. Mash until smooth and creamy. Season with salt and pepper to taste.
Once the lobster tails are done, remove them from the oven and drizzle with the reserved garlic herb butter. Garnish with a sprinkle of paprika if desired.
Serve the baked lobster tails alongside the creamy mashed potatoes, adding additional garlic butter on top if you like.