In a large bowl, combine the chicken, lemon zest, ½ tablespoon of lemon juice, ½ tablespoon of olive oil, ½ teaspoon of oregano, salt, and a few grinds of pepper.
Let the chicken marinate for about 10 minutes.
Preheat a grill pan, skillet, or wok over medium-high heat. Add a ½ tablespoon of olive oil, then add the chicken.
Grill or stir-fry until the chicken is cooked through, about 8 minutes, then transfer to a plate lined with paper towels.
In a small bowl, combine the yogurt, remaining ½ tablespoon of lemon juice, remaining tablespoon of olive oil, remaining ½ teaspoon of oregano, and a few grinds of pepper.
In a large bowl, toss the lettuce with a few spoonfuls of the dressing.
Divide the lettuce between two serving bowls and top with the chicken, tomatoes, cucumbers, and feta cheese.