In a medium bowl, whisk together lemon juice, dill, olive oil, garlic, salt, and pepper. Add chicken breasts, cover, and marinate in the refrigerator for at least 30 minutes.

Prepare quinoa or rice according to package instructions. Rinse quinoa, combine with water, bring to boil, then simmer covered for about 15 minutes.

Preheat grill over medium-high heat. Remove marinated chicken from the refrigerator and let rest for about 10 minutes. Grill for 6-7 minutes on each side until cooked through.

Prepare fresh vegetables: chop cucumber, halve cherry tomatoes, and thinly slice red onion. Soak onion in cold water if desired.

Slice grilled chicken into strips. In each bowl, layer quinoa or rice, followed by chicken and fresh veggies.

Drizzle with dressing if using, and serve warm or at room temperature. Garnish with lemon wedges and extra dill, if desired.