1In a large nonstick skillet, melt butter over medium heat. Toss apples with lime juice and pulp. Add apples in the skillet and sauté for about 2 minutes. Then cover with crumpled aluminum foil and simmer until the slices are just tender, about 4 minutes. Use a slotted spoon to transfer apples to individual serving dishes.
Add grape juice, lime peel, maple syrup or honey,,allspice and nutmeg to the skillet and boil, stirring constantly, until the mixture becomes a syrup, about 2-3 minutes.
Toast walnut by heating them in an ungreased nonstick skillet, shaking constantly, until they begin to brown and are fragrant.
Pour syrup over apples, sprinkle with walnuts and serve warm.