Fill a large pot with 4 quarts of water. Squeeze the lemon juice into the water and add the squeezed lemon halves. Add the Old Bay, garlic and onion. Tie the thyme sprigs together with kitchen twine and add to the pot. Cover and bring to a boil, then reduce to a simmer and cook about 5 minutes.
Add the potatoes to the pot and cook until just tender, about 10 minutes. Add the corn and cook 5 more minutes.
Meanwhile, slice along the back of each shrimp through the shells; remove the veins and rinse the shrimp. Add to the pot, cover and cook until the shrimp curl and are just opaque, 2 to 3 minutes. Transfer the shrimp and vegetables with a slotted spoon or skimmer to a large bowl. Add the butter and about 1 cup broth to the bowl and toss until the butter is melted. Transfer the shrimp and vegetables to a platter. Serve with the remaining broth, lemon wedges and hot sauce, if desired.