Cut the lobster tails in half lengthwise with a sharp knife. Combine melted butter and lemon juice in small mixing bowl. Brush mixture onto meat side of lobster tails. Lightly season with salt and fresh black pepper.
Place lobster tail splits onto the grill shell side down and cook for 5-6 minutes. To create the grill marks on the lobster meat, flip tail splits for 15-20 seconds at end of cook time, being careful not to overcook. Remove from heat and serve immediately.