Place the lentils in a large bowl, cover with boiling water, let stand 15 minutes, then drain and set aside.
Heat 2 tablespoons of the olive oil in a large Dutch oven or heavy pot over medium-high heat. Add the sliced Italian sausage and cook, turning occasionally, until browned on both sides, 5–7 minutes. Use a slotted spoon to transfer the sausage to a plate and set aside.
Add the remaining 2 tablespoons olive oil to the same pot. Add the chopped onions and cook over medium heat until translucent, about 5 minutes.
Add the chopped white parts of the leeks and the minced garlic; cook, stirring, 2–3 minutes more.
Add the diced carrots, diced celery, and diced bell peppers. Cook, stirring occasionally, until the vegetables begin to soften, about 8–10 minutes.
Stir in both cans of stewed tomatoes (including their juices) and the drained lentils.
Pour in the 2 quarts chicken broth, then add 1 teaspoon kosher salt, 1 teaspoon freshly ground black pepper, 1 tablespoon minced fresh thyme, 1 teaspoon cumin, the reserved browned sausage, and the Parmesan rind if using. Stir to combine and bring to a gentle boil.
Reduce heat to low, partially cover the pot, and simmer 45–60 minutes, or until the lentils are tender. Stir occasionally and check for doneness.
Remove and discard the Parmesan rind (if used). Taste and adjust seasoning as needed. Ladle into bowls and serve.