In a medium mixing bowl, combine plain yogurt, brown sugar, grated lime zest, lime juice, and salt. Whisk together until smooth, about 2 minutes.

Add cubed cooked chicken breast, green grapes, chopped mango, and watermelon to the yogurt mixture. Gently fold everything together using a spatula.

On serving plates, arrange a handful of torn Bibb or Boston lettuce to create a crisp base.

Scoop the chicken and fruit mixture onto the prepared lettuce. Ensure even distribution.

Sprinkle toasted chopped pistachios over each salad portion before serving.