Step 1Lightly salt the lamb chops and arrange them in a deep baking dish. Stir together the pomegranate juice and the vinegar. Reserve one-fourth cup of the mixture and pour the remaining 2 cups over the chops. Cover tightly with plastic wrap and refrigerate until ready to serve, at least 2 hours. Turn once to make sure the chops are evenly marinated.
Step 2In a covered medium saucepan, cook the apples, water, sugar, the reserved pomegranate-vinegar mixture and one-half teaspoon salt over medium-low heat until the apples are soft, 20 to 25 minutes (removing the lid the last 5 minutes to let the liquid evaporate if the apples are very juicy). Roughly mash the apples with a wooden spoon or a potato masher to make a thick, chunky sauce. Stir in the pomegranate seeds and rosemary and keep warm.
Step 3Heat a grill pan over medium-high heat. Pat the chops dry with a paper towel and cook them to medium, about 7 minutes per side.
Step 4Mound the applesauce in the center of a serving platter. When the chops are done, arrange them bone-side up leaning against the applesauce. Serve immediately.