Bring a large pot of salted water to a boil. Add baby potatoes; cook for 10-12 minutes until tender. Add corn and sausage in last 5 minutes.
Boil eggs for 8-9 minutes. Cool in ice water, peel, and set aside.
Pat lamb chops dry; season with oil, Cajun spices, paprika, salt, and pepper. Sear 3-4 minutes per side until browned.
Add butter to skillet; sear shrimp 2-3 minutes per side until pink.
Melt butter with olive oil; add garlic, seasonings, brown sugar, lemon, and hot sauce. Simmer 2-3 minutes, finish with parsley.
Arrange potatoes, sausage, corn, lamb, shrimp, and eggs in foil tray. Pour sauce evenly; toss gently to coat.
Cover with foil and bake at 375°F (190°C) for 10 minutes. Broil uncovered for 2-3 minutes to caramelize.
Garnish with parsley and lemon wedges; serve hot with garlic bread or rice.
