In a large bowl, whisk together lemon juice, red wine vinegar, olive oil, minced garlic, dried oregano, dried parsley, ground cumin, ground coriander, salt, and black pepper.
Add the chicken cubes to the marinade, ensuring they are evenly coated. Cover and refrigerate for at least 1 hour, or up to 3 hours for enhanced flavor.
Prepare the tzatziki sauce: Combine shredded cucumber, Greek yogurt, lemon juice, chopped dill, grated garlic, salt, and pepper. Mix well and refrigerate until ready to serve.
If using wooden skewers, soak them in water for at least 30 minutes.
Thread marinated chicken onto the skewers.
Preheat the grill to medium-high heat and lightly oil the grates to prevent sticking.
Grill chicken skewers for 3-4 minutes per side, or until internal temperature reaches 165°F (74°C).
Remove from grill and let rest for a few minutes before serving.
Serve warm chicken skewers with chilled tzatziki sauce. Optionally garnish with lemon wedges and fresh herbs.