Start by preparing the lobster tails. Using kitchen scissors, cut them along the top of the shell, down the middle, and to the tip of the tail.
Gently pull the shell apart so that the meat is exposed. Do this carefully to only separate it partially, and so you don't break the shell any further. Rinse the tails under cold water to wash away any shell remnants.
Start your smoker, aiming for a cooking temperature of 225°F.
While the smoker heats up, prepare the butter mixture. In a small saucepan over medium heat, melt the butter, lemon juice, black pepper, and minced garlic. Once the butter has fully melted, remove from heat and allow to cool.
Insert a skewer into each tail, starting at the exposed flesh and through to the tail fin at the other end. This will help prevent the tails from curling as they cook.
Place the tails on the smoker grates, with the slit side facing up. Cook for 45 minutes, or until the lobster meat's internal temperature has reached 145˚F (62°C). After 20 minutes, apply the butter to the tails, working it into the meat through the tail slit.
Use a meat probe to measure the internal temperature of the tails. When at 145°F, remove from the smoker and serve immediately.
(Optional) Finish on a high heat sear for 1-2 minutes, to give the tails grill marks.