Make the marinade: Combine all marinade ingredients in a large container. Add the chicken pieces and toss to coat. Marinate chicken for up to 1 hour at room temperature or up to 2 days in the fridge. Turn the chicken once during this time.
Make the tzatziki: In a food processor or blender, blend yogurt, garlic, salt, lemon juice, vinegar and herbs. If you want it spicy, add ½ jalapeno with the herbs. Blend until smooth. Transfer to a bowl and stir in the cucumber.
Preheat a grill over high heat or the broiler in the oven.
Thread the chicken pieces all with chicken and a few folded lemon slices and/or add vegetables, if you’d like. Discard marinade and onions.
Grill the kabobs for 10-12 minutes, turning occasionally. The chicken is done when the juice that runs out is clear rather than pink. You can allow these to rest for a few minutes on a platter, but cover them so they stay warm.
Spread a layer of lavash bread on a serving platter and place the kabob skewers on top. Place a piece of bread over each skewer and hold the chicken down while you pull out the skewer. Serve with green goddess tzatziki.