In a large, heavy saucepan, melt 4 tablespoons of butter over medium heat. Add flour and whisk to combine. Continue to cook, stirring constantly, until flour mixture is the color of peanut butter.
Add onions, celery, bell pepper, garlic, bay leaves, and thyme. Cook, stirring occasionally, until vegetables have softened, 6 to 8 minutes. Add stock, tomatoes, salt, cayenne, Worcestershire sauce, and Tabasco; bring to a boil. Skim surface, reduce heat, and simmer, stirring occasionally, for 30 minutes.
In a medium bowl, toss together crawfish tails (and any crawfish fat), and add to the simmering sauce along with the lemon juice, scallions, and parsley. Cook, stirring occasionally, for 15 minutes. Add remaining 2 tablespoons butter; stir to combine. Serve over rice.