Slice each Brussels sprout in half, cut each half into into strips, and discard the cores. Transfer to a large bowl.
Heat vegetable oil in a skillet over medium heat. Cook and stir bacon until browned and crisp, 8 to 10 minutes. Stir in cider vinegar, lemon juice, and brown sugar. Season with salt, black pepper, and cayenne pepper to taste. Increase heat to high and boil for 1 minute.
Pour hot bacon mixture over the bowl of Brussels sprouts and toss to coat completely. Season with salt and black pepper to taste.