Preheat a gas grill over medium-high heat to about 425 degrees. Cut 4 sheets of 12 x 14 inch aluminum foil. Place 1 Tbsp butter in the middle of each piece of aluminum foil.
Place potatoes on a plate and microwave on high power for 1 1/2 minutes, rotate and microwave 1 1/2 minutes longer. Or instead of microwaving, boil the potatoes for 6 - 8 minutes. Once cool enough to handle cut into slices. Divide potatoes among each of the four foil sheets (layering ingredients in center), followed by corn, sausage and shrimp.
Top each pile with another Tbsp of butter. Drizzle with lemon juice and sprinkle with thyme, garlic and Old Bay seasoning.
Fold up the foil packets by pulling up the two short ends together and folding over. Then push the ends up and shut so steam can't escape the packet. Grill sealed side up about 12 - 15 minutes or until potatoes are tender and shrimp have cooked through. Serve warm garnished with parsley.
These can also be cooked in the oven at 425 for about 15 minutes, or until shrimp have cooked through.