If using link-style chorizo, remove the sausage from its casings. Cook the chorizo in an enameled cast-iron or other heavy-bottomed deep-sided sauté pan or Dutch oven over high heat, using a spoon or spatula to break it up into crumbles, for 10 minutes or until browned and starting to become crispy. Using a slotted spoon, remove the chorizo from the pan and place it in a large bowl, leaving the grease in the pan.
Reduce the heat to medium and add the shrimp to the pan with the sausage grease. Cook the shrimp for about 3 minutes per side, until pink and no longer opaque. Transfer the cooked shrimp to the bowl with the cooked chorizo.
Add the chicken to the pan and cook for about 3 minutes per side, until slightly browned. Transfer the cooked chicken to the bowl with the shrimp and chorizo and set aside.
If there isn’t any grease left in the pan, add a tablespoon of butter. Turn the heat up to high and add the chopped celery, onion, and bell pepper. Sauté for about 10 minutes, until the onion is translucent and starting to brown and the bell pepper has softened. Add the garlic and cook for an additional 3 minutes, or until fragrant. Add the tomatoes, broth, coconut aminos, hot sauce, lemon juice, oregano, salt, onion powder, black pepper, and cayenne pepper. Stir to combine and bring to a simmer over medium heat.
Once the soup is bubbling, return the chorizo, shrimp, and chicken to the pan. Stir to combine and bring to a simmer once more. Season with more salt and cayenne pepper to taste.