In a bowl, whisk together 1 juice of 1 lemon, 2 tablespoons olive oil, 1 teaspoon oregano, 1 clove garlic (minced), and salt/pepper. Add cubed chicken breast and marinate for at least 30 minutes.
Heat a grill pan or outdoor grill to medium-high. Cook chicken 5-7 minutes per side until fully cooked. Let rest 5 minutes before slicing into strips.
While chicken rests, combine diced cucumbers and tomatoes in a bowl. Drizzle with remaining 1 tablespoon olive oil, a squeeze of lemon juice, and salt.
In a separate bowl, mix yogurt with remaining garlic clove, juice from 1 lemon half, finely grated cucumber (seeded), chopped dill (optional), and salt. Chill until ready to use.
Assemble bowls with a base of rice or quinoa, top with grilled chicken, cucumber-tomato salad, tzatziki, and optional pita wedges. Serve immediately or refrigerate components for meal prep.