Heat 2 tablespoons oil in a large skillet over medium-high heat. Add cauliflower, onion and ¼ teaspoon salt. Cook for about 5 minutes. Remove from heat and stir in ¼ cup dill.
Rub 1 teaspoon oil all over chicken. Sprinkle with ¼ teaspoon salt and ¼ teaspoon pepper. Grill, turning once, for about 15 minutes total.
Whisk the remaining 4 tablespoons oil, lemon juice, oregano, and the remaining ¼ teaspoon each salt and pepper in a small bowl.
Divide the cauliflower rice between 4 bowls. Top with the chicken, tomatoes, cucumber, olives, and feta. Sprinkle with remaining ¼ cup dill. If desired, drizzle with a vinaigrette and serve with lemon wedges.