Preheat a large pot over medium heat. Remove casings from sausage links if needed. Add sausage to the hot pot and break apart with a wooden spoon. Cook for 10-12 minutes, partially covering the pot halfway through cooking, until sausage is browned and cooked through. Transfer to a plate lined with paper towels. Reserve 1 tablespoon of drippings in the pot.
Return the pot to medium heat with the reserved drippings and butter. Once butter melts, add diced onions, celery, and carrots. Cook for 4 minutes, stirring occasionally, until vegetables are soft and onions are translucent. Add minced garlic and cook for 1 minute until fragrant.
Add flour and tomato paste to the pot. Stir constantly for 2 minutes to cook out the raw flour taste and concentrate the tomato flavor. The mixture will be thick and pasty.
Gradually add the chicken broth and beef broth in splashes, scraping the bottom of the pot with a silicone spatula after each addition to deglaze and incorporate the brown bits. Once all broth is added, stir in Worcestershire sauce, hot sauce, rinsed lentils, bay leaf, and all seasonings (basil, parsley, oregano, mustard powder, and black pepper). Mix well.
Increase heat and bring soup to a rolling boil. Once boiling, reduce heat to maintain a gentle simmer. Cover with lid slightly cracked and cook for 45 minutes, stirring every 10-12 minutes to prevent sticking.
Add the cooked sausage and drained diced tomatoes back to the pot. Stir well and simmer for another 10 minutes. If soup is too thick, add 1/2 cup water or extra broth to reach desired consistency. Remove bay leaf before serving. Taste and adjust seasoning if needed.