If you cut the chicken into smaller pieces before breading, they're nuggets—the guilt-free kind.
Place flour in a shallow bowl. Beat eggs in a second shallow bowl. Combine panko, Parmesan, and mustard powder in a third shallow bowl and season mixture with salt and pepper.
Season chicken with salt and pepper, then dredge in flour, shaking off any excess. Transfer to bowl with beaten egg and turn to coat. Lift from bowl, allowing excess to drip back into bowl. Coat with panko mixture, pressing to adhere. DO AHEAD: Chicken can be breaded 3 months in advance. Place between pieces of freezer paper or waxed paper and freeze in resealable freezer bags. Thaw before continuing.
Heat 6 tablespoons oil in a large heavy skillet or a cast-iron skillet over medium-high heat. Working in 2 batches, cook cutlets, adding remaining 2 tablespoons oil to pan between batches, until golden brown and cooked through, about 4 minutes per side. Transfer cutlets to a paper towel-lined plate and season with salt. Serve with lemon.