Heat oil in a 4- to 6-qt. pot over medium-high heat. Add celery (or fennel), carrots, bell pepper, 3 Tbsp. shallot, and garlic. Cook, stirring, until softened, about 3 minutes. Add tomato paste; cook, stirring, for 30 seconds. Add lentils, broth (or water), ½ tsp. pepper, and ¼ tsp. salt. Bring to a boil. Cover, reduce heat to low, and simmer until the lentils are tender, 35 to 40 minutes.
Meanwhile, combine parsley, lime juice, vinegar, and the remaining 2 Tbsp. shallot and ¼ tsp. each pepper and salt in a small bowl; stir well.
To serve, divide the stew among 4 bowls and top each with a dollop of the salsa verde. Pass the remaining salsa verde separately.
