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