Place sweetbreads in a medium mixing bowl; cover with cold water. Set aside to soak for 1 hour. Drain well; remove and discard white membrane.
Place sweetbreads, 1 1/2 tablespoons lemon juice, 1 teaspoon salt, and water to cover in a small Dutch oven. Bring to a boil. Reduce heat, and simmer 20 minutes. Drain well, and rinse with cold water. Cool sweetbreads completely.
Slice sweetbreads in half lengthwise; place on a well-greased rack in a shallow roasting pan. Broil 5 to 6 inches from heating element for 8 minutes. Transfer sweetbreads to a warm serving platter. Set aside.
Combine remaining 1 tablespoon lemon juice, 1/4 teaspoon salt, butter, parsley, onion juice, and pepper in a small saucepan. Bring mixture to a boil, stirring well. Remove sauce from heat, and pour over sweetbreads. Serve immediately.