Heat the olive oil in a large pot over medium heat. Add the onions, carrots, and celery. Cook for 3-4 minutes until the onions are translucent. Stir frequently.
Add the garlic and black pepper, cook for 1 minute, stirring frequently.
Add the kielbasa sausage to the pot and cook for 2-3 minutes, stirring frequently.
Add the lentils, broth, and water. Bring to a boil. Lower the heat, cover and simmer for 30 minutes. or until the lentils are tender. Stir occasionally.
When the lentils are soft lower the heat to low. Add the spinach and stir until it wilts.
Taste and add salt if needed. Serve the lentil sausage soup with bread or crackers, if desired.