Bring 4 cups water to a boil in a medium saucepan; add 1/2 teaspoon salt. Slowly whisk in the grits. Reduce the heat to a steady simmer and cook, whisking occasionally, until thickened, about 5 minutes. Whisk in 1 tablespoon butter and the cheese until melted. Season with salt. Set aside and cover to keep warm.
Meanwhile, season the shrimp with salt and the cayenne. Heat a large nonstick skillet over medium high heat; add 1 tablespoon butter. Add the shrimp and cook until opaque and lightly browned around the edges, about 2 minutes per side. Remove to a plate.
Add 1 tablespoon butter, the celery, bell pepper, garlic, scallion whites and a pinch of salt to the skillet. Cook, stirring occasionally, until the vegetables are crisp-tender, about 4 minutes. Add the tomato and cook until the pieces just start softening, about 1 minute.
Return the shrimp to the skillet along with the lemon juice, 2 tablespoons water and the remaining 1 tablespoon butter. Cook, tossing to coat, about 1 minute. Season with salt. Top each serving of grits with the shrimp and scallion greens.