Preheat your grill to medium-high heat, around 400°F (200°C).
In a mixing bowl, combine the melted butter, Cajun seasoning, minced garlic, lemon juice, paprika, salt, and pepper. Mix well until all ingredients are fully incorporated.
Using kitchen scissors, carefully cut the top shell of each lobster tail down the middle, stopping just before the tail fin. Gently pull apart the shell to expose the meat without detaching it completely.
Brush the exposed lobster meat generously with the Cajun butter mixture. Reserve some butter for basting during grilling.
Place the lobster tails shell-side down on the grill. Cook for about 5 to 7 minutes, basting occasionally with the reserved butter, until the meat is opaque and slightly charred.
Remove the lobster tails from the grill and let them rest for a few minutes. Garnish with fresh parsley before serving.