Preheat your grill or oven to 375°F (190°C).
Using kitchen scissors, cut the top shell of the lobster tail lengthwise.
Gently pull the lobster meat out of the shell, keeping it attached at the base.
Place the lobster meat back into the shell.
In a saucepan, melt the butter over medium heat.
Add minced garlic and sauté until fragrant, about 1 minute.
Stir in lemon juice, paprika, salt, and pepper.
Brush the garlic butter mixture generously over the lobster meat.
Place the lobster tails on the grill or in the oven.
Cook for 8-10 minutes, or until the lobster meat is opaque and cooked through.