Heat the olive oil in a large pot over medium heat. Add the onion, carrots, and celery. Cook for 5 minutes, stirring often, until the vegetables begin to soften.
Stir in the garlic and cook for 1 minute until fragrant.
Pour in the low-sodium vegetable broth. Add the white beans, rosemary, and black pepper. Bring the mixture to a gentle boil.
Reduce the heat and simmer for 15 minutes to let the flavors blend.
Add the kale and stir until it wilts, about 3 to 4 minutes.
Remove the pot from the heat and stir in the lemon juice before serving.