Wash sweetbreads in cold water, then put them in a large bowl, cover with ice water, and refrigerate for 2 hours, changing the water several times.
Put sweetbreads in a saucepan, cover with cold salted water, add lemon juice, and bring to a boil over medium heat. Boil for 1 minute. Drain, then transfer sweetbreads to a bowl of ice water to cool them. When cool, clean sweetbreads by removing and discarding all fat and sinew. Blot dry with a kitchen towel, wrap in plastic, and refrigerate overnight.
Preheat oven to 325°. Heat oil and 4 tbsp. butter in a large ovenproof skillet over medium heat until butter begins to sizzle. Generously season sweetbreads with salt and pepper, then saute until just browned, about 5 minutes per side. Add 3 tbsp. butter and transfer skillet to oven for 20 minutes. Remove skillet from oven, transfer sweetbreads to a platter and keep warm. Pour off fat, place skillet over medium heat, add vermouth, and cook for 1 minute, stirring with a wooden spoon to loosen any brown bits stuck to the bottom of the pan. Add stock and reduce by half.
Melt remaining 1 tbsp. butter in a large saute pan over medium heat, pour in 1⁄4 cup of sauce, then add asparagus, peas, haricots verts, onions, and carrots. Season to taste with salt and pepper. Cook until vegetables are heated through.
Arrange vegetables around sweetbreads on the platter. Spoon remaining sauce over sweetbreads, then sprinkle with parsley.