Heat 2 tablespoons of olive oil in a large pot over medium heat. Add the leek and cook until softened, about 5 minutes.
Add the garlic and cook for another minute until fragrant.
Add the lentils, tomatoes, sage, broth, salt, and pepper to the pot. Bring to a boil, then reduce heat and simmer for 30-35 minutes, or until the lentils are tender.
Stir in the spinach and cook until wilted, about 2 minutes.
Stir in the lemon juice and remaining olive oil. Taste and adjust seasonings as needed.