Preheat the oven broiler. Place a sheet of aluminum foil on a baking sheet, and coat with 2 tablespoons butter.
In a bowl, whisk together 1 teaspoon lemon juice, melted butter, mustard, raspberry vinegar, honey, tarragon, salt, and pepper.
Place the tilapia on the prepared baking sheet, and broil about 3 minutes in the preheated oven. Turn tilapia, and drizzle with about half the lemon juice dressing mixture. Continue broiling about 3 minutes, turn, and drizzle with remaining dressing. Continue broiling about 2 minutes, or until fish is easily flaked with a fork. Remove from heat, and sprinkle with remaining lemon juice to serve.