Drain pimiento, and press between paper towels to remove excess moisture. Combine pimiento and mayonnaise, stirring well. Combine 2 tablespoons pimiento mixture, crabmeat, 1/3 cup breadcrumbs, pepper, and egg white in a bowl; stir lightly. Set remaining pimiento mixture aside.
Shape crabmeat mixture into 4 (3/4-inch-thick) patties. Dredge patties in remaining 1/3 cup breadcrumbs. Place patties on a baking sheet; cover and chill 30 minutes.
Coat a large nonstick skillet with cooking spray; place over medium heat until hot. Add patties, and cook 4 minutes on each side or until lightly browned.
Place 1 lettuce leaf on bottom half of each bun; top with crab cakes. Spread remaining pimiento mixture evenly over crab cakes. Top with remaining bun halves. Serve immediately.