Preheat the oven to 425°F and line a large sheet pan with parchment paper.
Pat the chicken dry. Toss it with olive oil, brown sugar, smoked paprika, garlic powder, onion powder, cayenne, salt, and black pepper.
Add the lemon slices, spread the chicken in a single layer, and roast for 15 minutes.
Stir the chicken and roast for another 4 to 7 minutes, until the thickest piece reaches 165°F.
Mix the Greek yogurt, dill, parsley, chives, lemon juice, and salt. Fold in the shredded cabbage and rest for 10 minutes.
Warm the pitas, then fill them with slaw, roasted chicken, and diced avocado. Serve immediately.