To cook the lentils: In a large saucepan combine all the ingredients. Add water to the pot until it covers the ingredients by about 2 inches. Bring the water to a boil over medium heat, then reduce heat to a simmer. Cook for about 20 to 30 minutes or until the lentils are soft.
Remove the pot from the heat and season the water with salt. Taste the water to make sure it is seasoned. Let the lentils sit in the salty water for about 10 to 15 minutes. This will allow the lentils to absorb the seasoned water. Ladle off 1 cup of the lentil cooking water and reserve.
Remove all the vegetables and aromatics from the lentils and discard. Strain the lentils from the water.
To assemble the lentils: Place 2 tablespoons of olive oil in a large saute pan over medium heat. Add the bacon lardoons. When the bacon has rendered off a lot of fat and has become brown and crispy, add the onions. Season the onions with salt and sweat them until they become very soft and aromatic.
Add the celery, fennel and carrot. Season with salt and saute over medium heat until the vegetables start to become soft and aromatic, about 2 to 3 minutes. Add the garlic and saute for 1 to 2 minutes more. Add the cooked lentils, 1/4 of the reserved lentil cooking water, the mustard and vinegar. Cook until most of the liquid has reduced. Taste for seasoning, add salt or more vinegar, if needed. Serve hot or at room temperature.