In a small saucepan, cover lentils with about twice as much water, bring to a simmer and cook uncovered for about 30 minutes, or until just tender. (You can do this ahead of time and keep them in the fridge until you're ready for them.)
While the lentils are simmering, cook the bacon until crisp in a large, heavy skillet; transfer with a slotted spoon to a plate, leaving the drippings in the skillet. (If you like, pour them out and add a drizzle of canola or olive oil.) Add the leeks, celery, and carrot and cook, stirring often, for about 5 minutes. Add vinegar and cook until it's mostly evaporated. Drain the lentils well and add them to the skillet along with the spinach and tarragon; cook, stirring, until heated through and the spinach wilts. Season with salt and pepper and stir in the bacon.
Meanwhile, poach your eggs. Divide the warm lentil salad among 4 plates and top with the eggs.
Serving Size Serves 4.