Preheat grill. Set your grill up for two-zone grilling, with an overall temperature of around 350 degrees F.
Prepare lobster tails. Using a sharp knife, cut your tails open for grilling. Brush with melted butter, season with salt and pepper.
2 lobster tails, 1 Tablespoon unsalted butter, pinch Kosher salt, pinch black pepper
Grill lobster tails. Place the lobster tails shell-side up over indirect heat, then close the lid. Grill for 4-5 minutes, then flip with your tongs so the shells are down and grill 4-6 more minutes. You want your lobster to be slightly opaque and to have an internal temperature around 140 degrees F.
Cool and chop lobster. Transfer your lobster tails to a cutting board and allow them to cool completely. Toast your buns now on the grill, if desired. Once cooled, chop your tails and place in a large bowl.
Make dressing. Combine all the ingredients for your dressing in a medium-size bowl, then stir with a rubber spatula to combine. Add dressing to your chopped lobster, and stir gently until all the lobster is coated in dressing.
½ cup mayonnaise, 1 Tablespoon fresh lemon juice, 1 teaspoon lemon zest, 1 Tablespoon fresh dill, ¼ cup celery, ¼ cup green bell pepper, 1 Tablespoon fresh parsley, 1 Tablespoon fresh chives, Kosher salt, black pepper
Serve and enjoy. Your lobster salad can be enjoyed immediately as-is, or you can serve it on rolls. It also makes a creamy addition to salads and pastas.