Make the grits: Combine 4 cups water, the bay leaf, 1 teaspoon salt and a few grinds of pepper in a medium saucepan over medium heat. Bring to a simmer, then gradually add the grits, whisking constantly. Reduce the heat to medium low and cook, stirring occasionally with a wooden spoon, until tender, about 20 minutes. Discard the bay leaf. Stir in the heavy cream, butter and cheese. Remove from the heat; cover to keep warm. If the grits seem too thick, thin with water, 1 to 2 tablespoons at a time.
Meanwhile, make the shrimp: Heat the olive oil in a large skillet over medium heat. Add the sausage and cook, stirring, until browned, 2 to 3 minutes. Add the scallion whites, chopped celery and bell pepper and cook, stirring, until just starting to soften, about 3 minutes. Add the shrimp and season with salt. Cook, stirring, until the shrimp are almost cooked through, about 3 minutes.
Push the shrimp and vegetables to the edge of the skillet. Add the garlic, thyme and tomato paste to the center and cook, undisturbed, until sizzling, 1 minute. Add 1/2 cup water, the lemon juice and Worcestershire sauce and stir everything together. Bring to a simmer and cook until the shrimp are just cooked through and the sauce is slightly reduced, 3 minutes. Add the butter and swirl the pan until melted. Add the parsley, scallion greens and celery leaves and toss. Season with salt. Add more lemon juice, 1/2 teaspoon at a time, if needed.
Divide the grits among 4 shallow bowls. Top with the shrimp mixture.