First, warm the butter in a saucepan over low heat until melted. Skim off the solids and transfer the butterfat to a clean bowl.
Add all ingredients of clarified butter above to a small pot and melt, cooking for 20 minutes.
Hold the lobster tail with the hard top shell facing up and use kitchen shears to cut through the top shell and meat, stopping before the bottom.
Gently spread the tail halves apart, keeping the meat attached near the end.
Lift the meat, close the shell, and season with black pepper, paprika, and lemon zest.
Smoke the Lobster at 350°F for 15 minutes.
Baste the lobster with your prepared butter sauce twice, then cook for an additional 15 minutes or until it reaches 140°F.
Take the lobster out of the oven and let it rest for 10 minutes. Then serve and enjoy your scrumptious smoked lobster tails!