Preheat oven to 400°F. Line a baking sheet with parchment paper; place the bread on top. In a small bowl, whisk together olive oil, vinegar, lemon peel, and garlic. Brush the mixture evenly over the lavash (or pita); sprinkle with oregano. Season with salt and pepper. Bake until golden and crisp, 5 to 10 minutes. Break into pieces.
PREPARE THE VINAIGRETTE:
In a large bowl, whisk oil with vinegar and garlic; season with salt and pepper.
ASSEMBLE THE SALAD:
Put all salad ingredients in a bowl and toss with the vinaigrette. Serve with the toasted flatbread.