Prep: Preheat the oven to 325°F. Mix the Cajun Seasonings in a small bowl.
Cook Shrimp: Toss the shrimp with 1 1/2 teaspoons Cajun Seasoning in a medium bowl. Heat 1 tablespoon of oil in a 3.5 qt (or larger) braiser or Dutch oven over medium-high heat until shimmering. Cook the shrimp in an even layer just until opaque, about 2 minutes per side. Remove the shrimp to a plate using tongs. You can chop the shrimp tails off once they're cool enough to handle, if desired. Set aside until the end. Cook Sausage: Add the sausage to the pan in an even layer over medium heat. Brown on both sides, then transfer to a plate.
Season the Chicken: If using breasts, cover with plastic wrap and pound to an even thickness. Evenly season the chicken with 2 teaspoons of Cajun seasoning.
Cook the Chicken: Heat 2 tablespoons of oil in the sausage drippings over medium-high heat until shimmering. Add the chicken, and reduce the heat to medium. Cook until the internal temperature reaches 160 degrees F, about 5-7 minutes per side. Transfer the chicken to a cutting board and let it rest for at least 5 minutes before cutting it into 1/2-inch chunks. Set aside until the end.
Sauté Rice and Vegetables: Melt 2 tablespoons of butter in the drippings over medium heat. Add the rice and onions and sauté for 3 minutes. Add the bell peppers, celery, and the remaining Cajun Seasoning, and sauté for 3 additional minutes (the onions should be softened). Add the tomato paste and garlic and sauté for 60 seconds.
Add Ingredients: Add the broth, bay leaf, and tomatoes, and stir to combine.
Bake: Bring to a simmer over medium heat, uncovered. Stir everything, cover it, and place it in the oven. Bake for 10 minutes, then carefully check the rice for tenderness. If the rice isn't done, bake for an additional 2-5 minutes, or until cooked through, adding additional broth if needed.
Add Meats and Rest: Remove the pot from the oven, stir in the lemon juice, chicken, and sausage. (The rice will firm up as it rests - see science in post.) Top the rice with the shrimp, cover, and rest for 10 minutes undisturbed.
Garnish: Fluff with a fork, then serve hot, with sliced green onions and salt or hot sauce to taste.