In a small bowl, heat the cheese in the microwave for about 15 seconds. Stir in the mayonnaise.
Place the lavash on a work surface and spread with the cheese mixture. Divide the turkey among the bread pieces, arranging it over two-thirds of the surface closest to you. Layer the arugula, cucumbers and bell pepper in a row over the turkey. Starting from the edge closest to you, roll up the lavash into a tight log. Place on a platter, cover tightly with plastic wrap and refrigerate for 2 hours or overnight. Unwrap and slice crosswise into 1 1/4-inch tea sandwiches.