Put plain yogurt, fresh lime juice, curry powder, ground red pepper, and salt in a medium bowl, and stir with a whisk until smooth. Fold in the chopped turkey, chopped red bell pepper, fresh basil, and shredded matchstick carrots.
Arrange 1 1/2 cups of the mixed baby lettuce on each of 4 plates. Spoon 1 cup of the turkey salad on each plate of greens. Serve immediately.