In a large stockpot fitted with a basket insert, combine the stock ingredients and bring to a boil.
Add the potatoes, corn, and artichokes. Cover and bring back to a boil, about 5 minutes. Add the sausage, lemons, onions, and garlic, cover the pot and return to a boil, about 5 minutes. Taste the stock and adjust seasoning as needed. Add the crawfish and shrimp, cover, and turn off the flame. Allow the mixture to steep for 10 minutes. Add the asparagus, cover, and let steep until the vegetables and crawfish are tender, 5 to 15 minutes.
To serve, line a table with brown paper bags and newspaper. Lift the basket from the stock and drain. Dump the basket ingredients directly on newspaper. Serve with melted butter, beer, French bread, and paper towels.
Combine all ingredients thoroughly.
Recipe from "New New Orleans Cooking", by Emeril Lagasse and Jessie Tirsch, published by William and Morrow, 1993.