Combine first 5 ingredients in a small bowl. Stir well, and set aside. Combine carrot, celery, and cucumber in a bowl, and toss well.
Brush oil over tuna, and sprinkle with salt and pepper. Place a large nonstick skillet over medium-high heat until hot. Add tuna, and cook 3 minutes on each side or until desired degree of doneness. Remove from skillet, and cool. Cut tuna diagonally across grain into thin slices.
Arrange 1 1/2 cups carrot mixture on each of 4 plates; top with tuna slices. Drizzle 2 tablespoons vinaigrette over each serving. Garnish with red onion slices, celery leaves, and lemon slices, if desired.