Prepare grill for medium-high heat; brush grates with oil.

Melt butter in a small saucepan over medium-low heat.

Add garlic, cook until sizzling for 30 seconds.

Remove from heat, stir in lemon zest and juice.

Let cool slightly, then stir in parsley, chives, and cayenne.

Cut lobster shells lengthwise with kitchen shears.

Pull shells apart to expose lobster meat.

Skewer the tails to prevent curling while grilling.

Brush with olive oil and sprinkle lightly with salt.

Grill meat-side down for 4 to 5 minutes until shells turn red.

Flip and brush meat with butter. Cover grill lid.

Grill until meat is just white, about 3 minutes.

Flip again, brush with butter, and grill until cooked through.

Remove skewers and serve with extra warm butter.