Make the applesauce: Combine the apples, sugar and 1/2 cup water in a large pot. Bring to a simmer over medium-high heat. Reduce the heat to medium low, cover and cook, stirring occasionally, until the apples are very tender but still juicy, about 15 minutes. Remove from the heat and stir in the lemon juice. Mash the apples with a fork, or puree with an immersion blender or in a food processor for a smoother sauce. Transfer to a bowl and refrigerate at least 30 minutes.
Meanwhile, make the pork chops: Mix the paprika, garlic powder and sage in a small bowl. Season the pork chops with salt and pepper and rub all over with the paprika mixture. Heat a large nonstick skillet over medium-high heat and add the vegetable oil. Add the pork chops, reduce the heat to medium and cook until golden brown on the bottom, about 3 minutes. Flip and cook until browned on the other side and cooked through, 2 to 3 more minutes. Remove to a plate and pour off the drippings from the skillet.
Add the chicken broth and lemon juice to the skillet and scrape up any browned bits from the bottom of the pan. Add any juices from the plate of pork to the skillet and simmer until the sauce is reduced by half, 2 to 3 minutes. Stir in the butter until smooth. Transfer the pork chops to a platter and top with the pan sauce; sprinkle with parsley. Serve with the applesauce.