Bring a large pot of water to a boil. Add potatoes and corn and cook for 10 minutes, then drain.
In a large bowl, combine shrimp, par-cooked potatoes, corn, and sausage.
Add lemon juice, Old Bay, garlic, salt, pepper, and melted butter. Toss to coat.
Divide mixture among four heavy-duty foil sheets and seal tightly into packets.
Grill over medium-high heat for 10 minutes, flip, then cook 5 to 6 minutes more. Or bake packets on a sheet pan at 400°F for about 20 minutes.
While packets cook, melt 4 tablespoons butter over medium-low until foamy, then golden brown and nutty. Pour into a bowl for dipping.
Open packets carefully and serve with brown butter sauce.
Notes
Par-cook the potatoes and corn before sealing the packets so they turn tender. Seal the foil tightly so steam stays inside. Do not overcook the shrimp because residual heat continues cooking after the packets come off the grill or out of the oven. Watch the brown butter closely because it can burn quickly.