Prep the grill: Heat a gas or charcoal grill to medium-high, about 425–450°F.
Clean and oil the grates to prevent sticking.
Make the cowboy butter: In a bowl, mash the softened butter with garlic, Dijon, lemon juice and zest, parsley, chives, thyme, smoked paprika, red pepper flakes, cayenne (if using), salt, and pepper. Mix until smooth. Reserve 2 tablespoons for serving and keep the rest ready for basting.
Butterfly the lobster tails: Using kitchen shears, cut the top of the shell down the center to the tail fan.
Gently loosen the meat from the shell, lift it out, and rest it on top of the shell, keeping it attached at the tail. This helps it cook evenly and look great.
Season the meat: Pat the lobster dry. Brush with olive oil and season lightly with salt and pepper.
Grill shell-side down first: Place the tails on the grill, shell-side down.
Close the lid and cook for 4–5 minutes until the meat starts turning opaque around the edges.
Baste generously: Spoon or brush a layer of cowboy butter over the exposed lobster meat. Close the lid and cook 2–3 more minutes. The butter will melt into the meat and drip into the shell, basting from underneath too.
Optional flip: For a light char, flip meat-side down for 20–30 seconds.
Don’t overdo it—this is just to kiss it with flame.
Check doneness: The lobster is ready when the meat is opaque and firm, not translucent. Internal temp should be 135–140°F in the thickest part.
Finish and serve: Transfer to a platter. Top with the reserved cowboy butter and a squeeze of fresh lemon.
Serve hot.