Soak the raw sweetbreads in enough ice water to cover completely. Soak for 30 minutes before changing the water and soaking once more.
Preheat oven to 400 degrees Fahrenheit. Remove the sweetbreads from the ice water and bring 1 quart of chicken stock to a boil. Blanch the sweetbreads in the chicken stock, remove and let cool.
After sweetbreads have cooled, peel away the membrane and cut into 3 inch sections. Season generously with salt and pepper and dredge each piece in flour, shaking off excess.
Place canola oil and 2 tablespoons butter in a cast iron skillet. Add sweetbreads and bake until the sweetbreads are just pink in the center, and slightly firm to the touch, about 15 minutes. Remove from oven and top with 2 tablespoons butter.
Remove the sweetbreads from the pan and set aside. Place the skillet over low flame and add shallot. Deglaze with white wine and white wine vinegar, then add 1/2 cup chicken stop and capers. Cook over medium heat, stirring, until the sauce has reduced. Remove the sauce from the heat and add the remaining 1 tablespoon butter and lemon juice.
Return the sweetbreads to the sauce and toss to coat. Serve.
