For the herb compound butter: Add the butter, chives, tarragon, parsley, seafood seasoning, lemon zest and some black pepper to a bowl and gently blend together with a rubber spatula.
For the grilled Maine lobster tails: Prepare a grill for direct medium-high heat.
Using a sharp knife, cut the lobster tails in half lengthwise. Insert a skewer down through the tails so they stay straight. Place the tails on a baking sheet, drizzle with the olive oil and sprinkle with the salt and some black pepper. Slice the lemon in half and squeeze the juice over the tails.
Grill the tails cut-side down for 3 to 5 minutes. Flip over onto the shells, brush the compound butter generously on top and grill for another 3 to 5 minutes. Transfer to a platter and serve immediately with more herb compound butter on the side.