Dredge each fillet in the flour, dip it into the egg, then coat it completely with panko breadcrumbs. Set aside on a plate.
Heat a thin layer of oil in a large skillet over medium-high heat (about 350°F). Fry the breaded fish until golden and cooked through, about 3-4 minutes per side. Lightly toast the buns.
In a separate bowl, combine the light mayonnaise, sweet pickle relish, lemon juice, salt, and pepper. Stir well and set aside.