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, onion and thyme. 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.
TIP: No need to peel your shrimp - the shells are useful: They help flavor the broth, and they protect the inside of the shrimp from the heat, so you're much less likely to overcook them.