Butterfly your lobster tails and pull the meat out of the shell (instructions above).
Season the lobster meat with salt, pepper, and your all-purpose BBQ rub.
Place the lobster directly on the grates of your smoker with the meat-side facing upwards.
In a small pot or pan, combine the butter, garlic powder, and lemon juice.
Place the pot on the smoker next to the lobster. The butter should melt within 5 to 10 minutes, leaving you with a simple butter sauce for basting.
Baste the lobster every 10-15 minutes with the butter sauce.
After 45 minutes of cook time, or when the lobster reaches an internal temperature of 145°F, pull the lobster off the smoker and serve alongside the remaining butter sauce and an extra squeeze of lemon juice.