Toss apples with 1 tbsp lime juice in small bowl. Whisk remaining 2 tbsp lime juice, chutney (or preserves), and mustard together in a large bowl. Gradually whisk in the oil until incorporated. Season with salt and pepper to taste, and reserve 1/4 cup dressing in measuring cup.
Toss lettuce and watercress with remaining dressing in a large bowl and arrange on a large platter. Arrange apples, turkey, cheddar, walnuts, and cranberries on top of the lettuce. Drizzle salad with remaining dressing.