Heat the oven to 425°F and line an 18-by-13-inch rimmed sheet pan with foil. Toss potatoes with 1 tablespoon oil and the fine salt, spread cut-side down and roast for 20 minutes.
Mix paprika, garlic powder, celery salt, cayenne and pepper in a small bowl. Toss corn and andouille with remaining oil and half the spice mixture.
Turn potatoes and add corn and sausage to the pan. Roast for 12 minutes, keeping the pieces in one layer.
Pat shrimp dry and toss with the remaining spice mixture. Add to the pan, dot everything with softened butter and roast for 7 to 9 minutes until shrimp are opaque and reach 145°F and potatoes are tender.
Drizzle with lemon juice and turn everything gently through the pan juices. Divide potatoes, corn, sausage and shrimp among 4 plates.