Bring lentils and 4 cups salted water to a boil in a heavy 2-qt. saucepan over medium-high heat. Reduce heat to low; simmer 20 to 25 minutes or just until tender.
Meanwhile, cook potatoes in boiling salted water to cover 15 minutes or just until tender. Drain lentils and potatoes.
Cook bacon in a large, deep nonstick skillet over medium heat 6 to 7 minutes or until crisp; remove bacon, and drain on paper towels, reserving 2 Tbsp. drippings in skillet. Crumble bacon.
Add olive oil to hot drippings in skillet, and heat over medium heat. Sauté shallots, celery, and garlic in hot olive oil mixture 3 minutes. Remove from heat, and stir in vinegar and mustard. Season with salt and pepper to taste. Gently stir in lentils, potatoes, bacon, and parsley.