Make the marinade. In a large bowl or zip-top bag, whisk together the lemon juice, olive oil, honey, balsamic vinegar, garlic, oregano, salt, and pepper.
Marinate. Add the cubed chicken, toss to coat, cover, and refrigerate at least 30 minutes or up to overnight.
Prep. If using wooden skewers, soak them in water 20–30 minutes. Cut the bell pepper and red onion into 1-inch pieces.
Thread. Preheat the air fryer to 400°F (200°C). Thread the chicken onto skewers, alternating with pepper and onion, about four chicken cubes per skewer.
Air fry. Lightly spray the basket with olive oil. Arrange skewers in a single layer and air fry at 400°F for 5–7 minutes, flip, then cook 5 more minutes, until the chicken reaches 165°F (74°C).
Serve. Remove immediately, rest 2 minutes, garnish with parsley, and serve hot with tzatziki.