Place chicken cubes in a casserole dish or large bowl.
Combine yogurt, olive oil, lemon juice, and remaining marinade ingredients. Whisk well to combine. Pour over chicken. Toss so chicken is completely coated. Cover bowl and place in refrigerator to marinate for at least one hour or overnight.
To make gremolata, combine parsley, pistachios, lemon zest, garlic, lavender (if using), salt, and pepper. Add 1/2 cup of the olive oil and stir well. If needed, add the remaining olive oil. The gremolata should be spoonable and not too "dry." Cover and refrigerate until ready to serve.
To grill kebabs, prepare outdoor grill for direct heat on one side and indirect heat on other side; or have a grill pan ready to preheat if using stovetop. Thread the chicken cubes onto metal or pre-soaked bamboo skewers. (If using cooking indoors, preheat grill pan now.)
Arrange skewers over direct heat side of grill and cook for 3-4 minutes; turn over and cook for another 2-3 minutes, then move to indirect heat to continue cooking for 3-5 more minutes. (Using the indirect heat side prevents the chicken from burning on the outside before the inside is cooked properly.)
Transfer chicken kebabs to a serving platter. Drizzle some of the gremolata over the kebabs. Serve remaining sauce on the side.