PREHEAT barbecue to medium. Whisk oil with parmesan, lemon juice, garlic, mayo, Dijon, anchovies, sugar and Worcester- shire in a medium bowl. Set aside.
HEAT a medium frying pan over medium- high. Add bacon. Cook until crisp, 4 to 5 min. Transfer to a paper-towel-lined plate. Crumble into pieces when cooled.
HALVE each head of romaine lettuce lengthwise, forming a boat shape. Oil grill and barbecue lettuce, cut-side down, with lid open, until grill marks form on the underside of the lettuce, about 1 min. Transfer to a large plate. Drizzle each lettuce boat with 2 tbsp dressing. Sprinkle with crumbled bacon. Serve immediately. Dressing will keep well, refrigerated, up to 3 days.