Mix first 8 ingredients in small bowl to blend. Season dressing to taste with salt and pepper. Cook lobster tails in pot of boiling salted water until opaque in center, about 8 minutes. Drain and cool. Remove lobster meat from shells. Cut tail into 1/2-inch-thick slices. (Can be made 1 day ahead. Cover and refrigerate dressing and lobster separately.)
Divide endive among 4 plates. Top with lobster and garnish with tomato. Sprinkle with chives. Serve, passing dressing separately.
