Make Dressing: In a mixing bowl, whisk together the olive oil, vinegar, and mustard. Season with salt and black pepper. Once combined, set aside about 2 tablespoons of the dressing for later.
Cook Eggs: Bring a pot of water to a gentle boil over medium heat. Carefully add the eggs and cook for 6 to 7 minutes for soft centers. Transfer to cool water and let sit until cool enough to handle.
Prepare Lentils: If not already done, drain the cooked lentils in a strainer and allow them to cool slightly.
Mix Salad Base: In a large bowl, combine the lentils, diced carrots, chopped celery, red bell pepper, and green onions. Pour in the remaining dressing (not the reserved portion) and mix until everything is well coated.
Peel Eggs: Gently peel the cooled eggs and slice them in half.
Assemble Salad: Divide the arugula among serving bowls. Spoon the dressed lentil mixture over the greens.
Finish and Serve: Place the halved eggs on top of each salad. Drizzle with the reserved dressing and serve immediately.