In a small bowl, combine the farmer cheese, olive oil, lemon zest, lemon juice, Italian seasoning, salt, and several grinds of black pepper.
Lay the lavash breads on a clean work surface. Spread ¼ cup of the farmer cheese mixture over each lavash, leaving a small border around the edges.
Top each lavash with ½ cup baby spinach, 4 ounces shredded chicken, and ¼ cup roasted red peppers.
Carefully fold in the short sides of each lavash, then gently roll it up like a burrito. Handle the lavash carefully as you work because it can tear easily.
Serve the wraps immediately or refrigerate until chilled.
To serve warm, reduce the oven temperature to 400°F. If using jarred roasted red peppers, preheat the oven to 400°F. Place the wraps seam-side down on a baking sheet and bake for 10 to 15 minutes, turning halfway through, until warmed through and lightly crisp.
Cut each wrap in half or serve whole.