In a large, heavy saucepan, melt 4 tablespoons of the butter and whisk in flour to combine well. Continue to cook, stirring constantly, until roux is a peanut butter color.
Add onions, celery, bell pepper, garlic, bay leaves, and thyme and cook until vegetables are soft, about 6 to 8 minutes. Add stock, tomatoes, salt, red pepper, hot sauce, and Worcestershire sauce and bring to a boil.
Skim surface, reduce heat to a simmer, and cook uncovered for 30 minutes, stirring occasionally.
Add crawfish tails and fat, lemon juice, green onions, and parsley and cook for 15 to 20 minutes, stirring occasionally. Add remaining butter and stir to combine well. Taste and adjust seasoning if necessary. Serve over hot rice.