In a large mixing bowl, combine the cooked chicken, diced cucumber, cherry tomatoes, and red onion.
In a separate small bowl, whisk together the Greek yogurt, mayonnaise, Dijon mustard, dill, lemon juice, salt, and pepper until smooth.
Pour the dressing over the chicken and vegetable mixture. Gently toss until everything is well coated.
Taste and adjust seasoning if necessary. If the salad is too thick, you can add a little more lemon juice or a splash of water to reach your desired consistency.
Serve the salad on a bed of lettuce leaves if desired, or enjoy it on its own.