grated parmesan or romano cheese, for serving(optional)
Heat the bacon fat, butter, or olive oil in the bottom of a large Dutch oven over medium-high heat. Add the onion, celery, carrots, and garlic. Season the vegetables well with salt and pepper. Cook, stirring occasionally until the vegetables have softened, about 10 minutes. Add the tomato paste and stir to coat the vegetables. Cook until the tomato paste darkens and sticks a bit to the bottom of the pot, about 2 minutes more.
Add the chicken broth and lentils and bring to a boil. Reduce the heat to maintain a very gentle simmer and add the chicken. Cover and continue cooking for 1 hour, checking periodically to make sure the soup isn't bubbling too vigorously. Transfer the chicken thighs to a plate to cool.
Using 2 forks, shred the chicken and return it to the pot. Taste and season with salt and pepper as needed. Serve with cheese sprinkled over the top if desired.