Heat the olive oil in a large pot over medium heat. Add the fennel sausage and cook, breaking it up with a spoon, until browned.
Add the onion, carrots, and celery. Cook for 5 minutes until the vegetables soften.
Stir in the garlic and cook for 1 minute.
Add the lentils and chicken broth. Bring the mixture to a boil, then reduce to a simmer.
Cover and cook for 25 minutes, stirring occasionally, until the lentils are tender.
Stir in the white beans, rosemary sprigs, salt, and black pepper. Simmer uncovered for 10 more minutes.
Remove the rosemary sprigs before serving.