1Heat coals or gas grill for direct heat. In small bowl, mix all lemon mayonnaise ingredients until well blended.
2Cut bread horizontally in half. Drizzle 1 tablespoon of the oil over cut sides of bread. In small bowl, mix remaining 1 tablespoon oil, the lemon peel, soy sauce and lemon pepper seasoning. Rub both sides of beef with oil mixture.
3Cover and grill beef over medium heat 8 to 9 minutes, turning once or twice, until desired doneness. Add bread, cut sides down, for last 2 minutes of grilling or until toasted.
4Spread mayonnaise on bottom half of bread. Cut beef crosswise into thin slices. Layer lettuce and beef on bottom half of bread. Add top half of bread; cut crosswise into 4 sandwiches.