Place crawfish in a large metal basket insert that fits a 10- to 15-gallon pot. Rinse crawfish well and set aside in basket.
Bring water to boiling in pot. Add crawfish Seasoning bags, half of the salt, and half of the ground red pepper; stir to mix. Add potatoes and cook for 15 to 20 minutes or until almost done; remove potatoes from pot. Stir in remaining salt and pepper, and add basket of crawfish. Squeeze the lemons over crawfish, then add the squeezed lemons, onions, and corn to the pot.
Return water to boiling and cook for 2 to 3 minutes. Turn off heat, cover pot, and soak for 15 to 30 minutes. The longer the crawfish soak, the more seasoning they'll absorb. Begin testing for desired seasoning level after 10 minutes by removing one or two crawfish from pot, letting them cool slightly, peeling, and tasting.
Return potatoes to pot during the last 5 minutes of soaking. Remove basket from pot. Serve hot crawfish and vegetables with Tangy Dipping Sauce. Makes 6 to 8 servings.