Season chicken breasts with lemon pepper on all sides. Place on grill and cook for about 6 minutes on each side, until chicken has reached internal temperature of 160 degrees F and is no longer pink in the middle. When you flip the chicken, drizzle with lemon juice.
While chicken is cooking, whisk together the mayonnaise, lemon zest, and basil. Serve the grilled chicken with aioli on the side.