Preheat the oven to 425 degrees F. To a medium bowl, add the olive oil, lemon zest & juice, garlic, dill, oregano, 1 ½ teaspoons kosher salt & ground black pepper as desired. Whisk to combine well. Add the chicken to the bowl, tossing to coat in the marinade. Set aside to marinate for 15-20 minutes at room temperature while the oven preheats. (Alternatively, you can cover & marinate in the refrigerator for up to 6 hours.)
Place the marinated chicken on a small baking sheet. Transfer to the oven & roast 10-15 minutes, or until cooked through.
If desired, broil the Greek-inspired chicken for a crispy, browned finish. Remove the chicken from the oven & preheat the oven's broiler to its highest setting. Transfer the roasted chicken to a cutting board & carefully slice into bite-sized pieces. Place the sliced chicken back on the baking sheet. Place the baking sheet under the broiler. Broil 4-5 minutes, carefully turning the pan halfway through, until the chicken is browned & slightly crisp. Remove from the oven & set aside for serving.
Place the grated cucumber in a medium bowl & set aside. To a food processor, add the avocado, garlic, lemon juice, dill, & Greek yogurt. Season with S&P as desired. Pulse to break up the avocado, then blend until smooth & creamy. If necessary, add a couple tablespoons water to smooth out texture. Transfer the creamy avocado mixture to the bowl with the grated cucumber. Fold to combine well. Set aside.
Build your avocado tzatziki bowls as desired. I like to swoop the avocado tzatziki directly along the sides of the bowl, then create a base of lemon herb rice & finely shredded lettuce, & top it all off with the roasted chicken, diced cucumbers, cherry tomatoes, feta, & pickled red onions.