Cover lentils with cold water by 2 inches in a saucepan, then simmer, uncovered, until just tender, about 20 minutes.
While lentils are simmering, cook bacon in a 12-inch nonstick skillet over moderate heat, stirring, until crisp, then transfer with a slotted spoon to paper towels to drain, leaving fat in skillet. Add leeks, celery, and carrot to skillet and cook, stirring, until just tender. Add vinegar and boil until most of liquid is evaporated. Remove skillet from heat and stir in tarragon, half of bacon, and salt and pepper, to taste. Transfer to a bowl and keep warm, covered, reserving skillet.
Drain lentils well in a large sieve. Stir into vegetable mixture and season with salt and pepper. Keep warm, covered.
Wipe skillet with paper towels, then add oil and heat over moderate heat until hot but not smoking. Fry eggs in batches until whites are just set but yolks are still runny and season with salt and pepper.
Divide lentil salad among 4 plates. Top with spinach, eggs, and remaining bacon.
Cook's Note: Serving eggs with runny, not fully-cooked, yolks may be of concern if salmonella is a problem in your area.
Recipe courtesy of Gourmet Magazine