Heat grill to medium-high. In a small bowl, whisk together the preserves, the lemon zest, 3 tablespoons lemon juice, the Dijon mustard, and the rosemary. Reserve all but 2 tablespoons glaze.
In a large bowl, whisk together the oil, the horseradish, 2 tablespoons apricot glaze, remaining 2 tablespoons lemon juice, and 1/4 teaspoon each salt and pepper. Add the shallot; toss to coat.
Cut the pork into 1-inch pieces. Cut each apple into eight wedges, then cut the wedges in half crosswise. Thread the pork and apples onto eight 8-inch skewers. Rub with oil and season with 1/4 teaspoon each salt and pepper.
Grill the skewers, turning occasionally, for 3 minutes. Brush with the glaze and continue grilling, turning and brushing occasionally with the glaze until just cooked through, about 3 minutes more.
Toss the shallots and dressing with the lettuce and serve with the skewers.