Place first 7 ingredients on a double layer of cheesecloth. Gather edges of cheesecloth together; tie securely.
Combine cheesecloth bag, water, salt, All That Jazz Seasoning, paprika, and ground red pepper in an extra-large stockpot, and bring to a boil. Cover, reduce heat, and simmer 15 minutes.
Add the potatoes, onions, lemons, and garlic. Cover and return to a boil; cook 10 minutes. Add the corn and crawfish. Cover and return to a boil; cook 15 minutes or until done. Let stand 30 minutes. Drain; discard cheesecloth bag.