Place the live crawfish in a large cooler or tub and cover with cool water. Stir gently with a long spoon or gloved hands, then drain. Repeat 2–3 times until the water runs mostly clear. Remove and discard any dead crawfish that are not moving.
Scrub the potatoes, cut the corn into thirds, and slice the sausage into 1–2 inch pieces. Peel and quarter the onions and halve the head of garlic horizontally. Have all add-ins ready before you start boiling.
In a large stockpot or outdoor boil pot, add the water, seafood boil seasoning, kosher salt, squeezed lemon juice and lemon halves, onions, halved garlic head, bay leaves, peppercorns, hot sauce, and cayenne. Bring to a strong boil over high heat. Taste the broth and adjust salt and spice so it is boldly seasoned.
Add the potatoes to the boiling seasoned water and cook for 10–12 minutes, until just starting to become tender when pierced with a fork. Add the sliced sausage and cook for another 5 minutes.
Add the corn pieces to the pot and cook for 5 minutes. The broth should be very fragrant at this point.
Carefully add the live crawfish to the pot, being careful to avoid splashing. Stir with a long-handled spoon or paddle to submerge them evenly. Return the water to a boil and cook for 3–4 minutes. If using shrimp, add them during the last 3–4 minutes of boiling so they cook just until opaque.
Turn off the heat, cover the pot, and let the crawfish soak in the hot seasoned water for 20–30 minutes so they absorb flavor. For a spicier boil, extend the soak to 30–40 minutes, tasting a crawfish tail occasionally to check seasoning.
While the crawfish soak, melt the butter in a small saucepan over low heat. Add the minced garlic and cook gently for 3–4 minutes until fragrant but not browned. Stir in paprika, Cajun seasoning, lemon juice, and chopped parsley. Season with salt and black pepper to taste and keep warm.
Using a large strainer basket or slotted tools, carefully remove the crawfish, potatoes, corn, and sausage from the pot and drain well. Cover a large table with newspapers or butcher paper and pile the boil mixture in the center. Drizzle the garlic butter over the top or serve it on the side for dipping.
To eat, twist the tail from the head of each crawfish, peel the shell from the tail, and enjoy the meat. Optionally, suck the juices from the head for extra spicy flavor. Serve with cold drinks and simple sides.