Dice onion, carrots, and celery into ¼-inch pieces; mince garlic; rinse lentils in a fine-mesh strainer and remove any debris; remove sausage casings; roughly chop spinach or kale.
Heat a large Dutch oven over medium-high heat, add olive oil, then add sausage. Cook 6–8 minutes, breaking it into ½–1 inch pieces, until deeply browned. Do not drain unless there is more than 2 tablespoons of fat.
Reduce heat to medium, add onion and cook 5 minutes until softened, then add carrots and celery and cook 4–5 more minutes. Push vegetables aside, add garlic to the center, and cook 30–60 seconds until fragrant.
Stir in the rinsed lentils and canned diced tomatoes with their juice, scraping up any browned bits from the bottom of the pot with a wooden spoon.
Pour in chicken broth and water, then add bay leaves, thyme, oregano, smoked paprika, red pepper flakes (if using), 1 tsp salt, and ½ tsp black pepper. Stir well and bring to a boil over high heat.
Reduce heat to medium-low, partially cover, and simmer 35–40 minutes, stirring every 10 minutes, until lentils are tender but still hold their shape. Add more water or broth if soup becomes too thick.
Taste and adjust salt and pepper, remove bay leaves, then stir in the spinach or kale and cook 1–4 minutes until wilted. Turn off heat and stir in fresh lemon juice.
Let soup rest off heat for 5–10 minutes, then ladle into bowls and garnish with fresh parsley. Serve with crusty bread for dipping.