In a medium saucepan, combine the grits with the water and milk over medium-low heat and bring to a boil, then reduce to simmer. Cook, stirring occasionally, until tender and creamy, about 10-15 minutes. Stir in the salt and the cream and keep warm until ready to serve.
Place the shrimp in a large bowl and season with the cajun seasoning, tossing to cover evenly. Set aside.
Heat a large skillet over medium high heat. Slice the andouille sausage in half lengthwise and then into 1/2 inch thick half moons and add to the skillet. Cook for 4-5 minutes, stirring occasionally, until the sausage is browned. Transfer to a bowl and set aside.
In the same skillet, cook the cut bacon until cooked through. Use a slotted spoon to remove the bacon from the pan and add to the bowl with the sausage. Pour all but 1 tablespoon of the fat into a small bowl and set aside.
Sprinkle the shrimp with 1/4 cup of the flour and toss to coat. Tap the excess flour from the shrimp and place in the skillet taking care not to crowd the pan, cooking for 2-3 minutes on each side. Cook the shrimp in batches if needed. Transfer the shrimp to another bowl and set aside.
Add 1 tablespoon of the reserved bacon fat to the skillet and set the heat to medium high. Add the onion, celery, garlic and bay leaf and cook for 4-5 minutes or until the vegetables have softened. Sprinkle 2 tablespoons of the flour over the vegetables. Crush the dried thyme between your fingers and add to the veggies, and stir to evenly coat the veggies. Cook for another 2-3 minutes, stirring occasionally.
Add the sausage and bacon back to the skillet, then add the clam juice, chicken broth, and the tomatoes, stirring into the vegetables and decreasing the heat to medium-low.
Simmer for 10 minutes or until the sauce is thick enough to cover the back of a spoon and the tomatoes are just about to burst.*
Return the shrimp to the pan. Add half of the chopped green onions, Tabasco, Worcestershire, and lemon juice. Discard the bay leaf and swirl in the butter.
Spoon a serving of the warm grits into a bowl and ladle with a few shrimp and some sauce. Garnish with chopped green onion and parsley.
*Add more chicken broth if you prefer a looser gravy. If your gravy is too thin, add 1 tablespoon of flour to 1/4 cup of the sauce in a small bowl, mix well, then whisk into the gravy to thicken it.