Bring 4 cups of water and 2 tablespoons salt to a boil in a 5-gallon stockpot. Place a vegetable steamer or rack in the bottom of the pot. Add lobsters; steam, covered, for 14 minutes or until done. Remove meat from cooked lobster claws. Cut each lobster tail in half, lengthwise; chill meat and tails.
Place potatoes in a saucepan; cover with water. Bring to a boil; cook 5 minutes or until tender. Drain; set aside.
Preheat oven to 300°.
Combine remaining 1 cup water, stock, wine, and tomato paste in a large saucepan; bring to a boil. Cook over medium-high heat 30 minutes or until reduced to 5 cups. Stir in remaining 1/8 teaspoon salt and pepper.
While stock reduces, place lobster and potato in a single layer on a baking sheet, keeping separate. Bake at 300° for 20 minutes or until thoroughly heated. Place half a lobster tail in each of 8 shallow soup bowls; place 1/2 cup potato and 1/4 cup chopped lobster in each bowl. Ladle about 2/3 cup stock mixture over each serving; sprinkle each serving with 3/4 teaspoon tarragon and black pepper.