Season the chicken with salt and black pepper and let it stand for 15 minutes.
Place the flour in a shallow bowl, beat the eggs with water in a second bowl and combine the panko with Parmesan in a third.
Coat each cutlet in flour, dip it in egg and press it firmly into the Parmesan panko, then rest the breaded chicken for 10 minutes.
Whisk the mayonnaise and lemon juice together and set the sauce aside.
Heat the canola oil in a wide heavy skillet to 350°F and shallow-fry 2 cutlets at a time for 3 to 4 minutes per side, keeping the oil above 335°F, until golden and 165°F inside.
Drain the cutlets on a wire rack and rest for 3 minutes.
Toast the ciabatta cut sides, spread them with lemon mayo and assemble each roll with 1 cutlet and 1/2 cup arugula.