While I'm not one that's much for seafood, I do have a Weber grilling book that has not steered me wrong yet. They have a recipe for lobster tails if you would like:
1 1/4 cups (2.5 sticks) unsalted butter
2 tablespoons finely chopped fresh basil
1 tablespoon grated lemon zest
1 tablespoon fresh lemon juice
1/2 teaspoon hot sauce
1/2 teaspoon kosher salt
I assume you probably know how to cut these lobster tails, using shears to cut both sides of the shell length wise and then use a knife to cut them in half.
melt the butter. when melted, skim off foam. stir in remaining ingredients and heat for one minute. remove from heat and pour off 1/4 cup of the butter to use for grilling the lobster. Cover the saucepan to keep the remaining butter for serving.
Brush the meat side of the lobster with some butter. Grill the lobster tails meat side down over direct heat (350-450) for 2-3 minutes. Brush the tops of the shell with some more butter, turn them over, and grill until the meat is white and firm but not dry, 5-8 minutes more. Remove from the grill and serve with the reserved butter.
geek, dad, noobie griller. The arsenal:Master Forge 32-in Charcoal Grill