In a large Dutch oven or soup pot, cook the chopped bacon over medium heat until crisp. Remove the bacon with a slotted spoon and set aside, leaving about 1 tablespoon of the drippings in the pot. Add the olive oil if needed.
Add the diced onion, carrots, and celery to the pot. Cook for 5 to 7 minutes, stirring occasionally, until the vegetables begin to soften. Stir in the minced garlic and cook for 30 seconds until fragrant.
Add the rinsed lentils, diced tomatoes, broth, cumin, paprika, bay leaves, salt, and black pepper. Stir everything together, then return most of the cooked bacon to the pot, reserving a little for garnish if desired.
Bring the soup to a boil, then reduce the heat to a gentle simmer. Cover and cook for 30 to 35 minutes, or until the lentils are tender.
Remove the bay leaves and stir in the vinegar. Taste the soup and adjust the salt and pepper as needed.
Ladle into bowls and garnish with chopped parsley or cilantro, extra bacon, Parmesan cheese, or a drizzle of olive oil if desired.