1. Place lentils in a medium saucepan. Cover with water to 3 inches above lentils; bring to a boil. Reduce heat, and simmer 20 minutes or until lentils are tender. Drain and keep warm.
2. Add water to a large saucepan to a depth of 3 inches; bring to a boil. Add eggs; boil 5 minutes and 30 seconds. Drain. Plunge eggs into ice water; let stand 5 minutes. Drain and peel.
3. Combine oil, vinegar, mustard, garlic, salt, and 1/4 teaspoon black pepper in a medium bowl, stirring with a whisk. Set aside 2 tablespoons oil mixture. Add lentils, bell pepper, onions, and celery to remaining oil mixture; toss gently to coat. Place reserved 2 tablespoons oil mixture and arugula in a large bowl; toss to coat.
4. Place about 3/4 cup lentil mixture and about 1 cup arugula mixture on each of 6 plates. Cut eggs in half lengthwise; top each serving with 2 egg halves. Sprinkle evenly with remaining 1/8 teaspoon black pepper.