Wash the red Delicious and Granny Smith apples thoroughly under cool water. Core and slice them into matchstick pieces, about 1/4 inch thick.

Drizzle freshly squeezed lemon juice over the sliced apples, tossing gently to coat each piece and prevent browning.

In a separate bowl, combine matchstick carrots, finely diced yellow onion, and dried cranberries, mixing thoroughly.

Add the soaked apples to the carrot mixture and stir gently to incorporate all elements.

In a small bowl, mix vanilla yogurt and mayonnaise until smooth, then add sugar, salt, and pepper to taste.

Pour the dressing over the salad mixture and mix thoroughly to ensure even coating.

Fold in the mandarin segments gently, being careful not to break them apart.

Cover the salad and refrigerate for at least 3 hours to allow flavors to meld.

Serve in a bowl, garnished with additional cranberries or mandarin segments if desired.