In a large bowl, combine bread crumbs, egg, salt and pepper. Add beef; mix lightly but thoroughly. Shape into four 1/2-in.-thick patties. Press a shallow indentation in the center of each with your thumb. Brush both sides of patties with oil.
Grill burgers, covered, over medium heat or broil 4 in. from heat 4-5 minutes on each side or until a thermometer reads 160°. Serve on buns, topped with crab, cocktail sauce and a squeeze of lemon juice.