For the chicken skewers:
Combine the lemon juice, olive oil, oregano, salt, sugar, pepper and garlic, along with 1 tablespoon of water, in a bowl. Add the chicken pieces and toss to coat. Marinate for at least 30 minutes or up to 8 hours.
Heat a grill or grill pan over medium or preheat the broiler.
Remove the chicken from the marinade and thread the chicken pieces, red bell pepper and red onion onto 4 skewers.
If grilling, place the chicken on the grill and cook for 5 minutes on each side or until chicken is cooked through.
For broiling, broil for 8-10 minutes or until chicken is cooked through.
While the chicken is cooking make the sauce.
For the yogurt sauce:
Mix together the greek yogurt, olive oil, cucumber and parsley. Season with salt and pepper to taste. Refrigerate until ready for use.
Serve the chicken skewers with the yogurt sauce. Garnish with parsley and lemon wedges if desired.