In a small saucepan melt butter. Add curry powder and chilli pepper; heat for 1 to 2 minutes. Add salt and pepper to taste.
Rinse lobster tails and pat dry. Turn lobster tails shell side down. To expose meat, cut lengthways through bottom shell with kitchen shears or sharp knife. Bend tail along cut to crack open shell a little wider. (You can also cut bottom shell lengthways along each side and remove.) Sprinkle 1/2 tablespoon lime juice on meaty portion of each lobster tail. Spread 1 tablespoon of butter mixture on each lobster tail. Reserve remaining butter mixture.
Place lobster tails shell side down on centre of cooking grate. Grill 8 to 10 minutes or until meat is opaque. Serve with remaining butter mixture, if desired.