Preheat your smoker to 225°F/105°C.
Place a small cast iron pan on the grill or on the stovetop. Add butter, oil, garlic, lemon juice, paprika, minced thyme, pepper flakes, salt, and pepper.
Stir it for about 30 seconds until the butter melts. Add the parsley and set aside.
Using kitchen shears or scissors, cut the top of the lobster shell lengthwise down the center up to (but not through) the tail.
Give the meat a quick rinse and remove any grit or dirt if necessary.
Flip the lobster tail over and gently press down on the ribs or belly to help release the meat.
Brush the lobster meat with the butter/garlic mixture, making sure all parts are covered with the sauce.
Once your smoker has preheated, place the lobster tails on the grate, meat side up.
Cook for 45 minutes or more, depending on the size of the lobster tails.
They're done when the tail meat turns from translucent to white (or the internal temperature reads 145°F/63°C).
Remove and serve immediately with the leftover garlic mixture.