Cook's Note: You can buy large, frozen tiger shrimp that have been deveined but are still in the shell. If you use these, thaw them according to the package directions. If using fresh shrimp, you can ask the person at the fish counter to devein them for you in the shell. You can also do this yourself: Using kitchen shears, cut the shell along the vein and pull the vein out with your fingers. Or, you can just skip the deveining process. The vein won't hurt you.
Combine 3 tablespoons of the chili powder and 1 tablespoon of the salt in a small bowl. Rub the shrimp with this mixture, making sure you rub some into the open cut where the shrimp as been deveined (if applicable) to season the shrimp inside the shell. Place the shrimp in a shallow, non-reactive pan, cover with plastic wrap and refrigerate while you make the sauce.
In a saucepan set over medium-high heat, melt the butter. Add the onion and garlic and cook for 3 to 5 minutes, until soft, but not browned. Add the ketchup, oil, brown sugar, Worcestershire sauce, lemon, lemon juice, bay leaves, oregano, thyme, and cayenne, as well as the remaining 2 tablespoons chili powder and 2 teaspoons salt. Stir to mix. Reduce the heat to a simmer, and cook, covered, stirring occasionally, for about 20 minutes, or until thick. Remove from the heat, uncover, and cool to room temperature. Remove and discard the lemon slices and bay leaves. Pour 1 1/2 cups of the sauce over the shrimp. Toss to coat well. Cover and refrigerate the shrimp for 1 to 2 hours. Cover and refrigerate the remaining sauce separately and save for dipping.
Prepare a charcoal fire or preheat a gas grill for direct grilling over high heat.
While the grill is heating, reheat the remaining sauce in a small, covered saucepan over very low heat, it will only take a few minutes. Watch the sauce carefully so that it doesn't burn.
Remove the shrimp from the pan and discard the marinade. Grill the shrimp for 2 to 3 minutes per side, until the shells are orangey-pink. To test for doneness, take a shrimp off the grill, remove the shell and cut the shrimp in half: The flesh should be white and firm throughout.
Serve with the warm sauce for dipping, and a large bowl for the shells.
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