1. Combine lemon juice and minced garlic in a bowl and let stand for 10 minutes. Process mayonnaise, 1/4 cup Parmesan cheese, lemon-garlic mixture, vinegar, Worcestershire, mustard, anchovies, salt, and pepper in a blender for 30 seconds. With blender running, slowly add in 1/4 cup olive oil.
2. If cooking on a charcoal grill, open the bottom vent completely. Light large chimney starter filled with charcoal briquettes (six quarts). When top coals are partially covered with ash, pour evenly over half of grill. Set cooking greate in place, cover, and open lid vent completely. Heat grill until hot, about 5 minutes.
3. If using a gas grill, turn all burners on high, cover, and heat grill until hot (about 15 minutes). Leave all burners on high.
4. For the salad, clean and oil cooking grate. Brush bread slices with oil and grill, uncovered, until browned (about one minute per side). Transfer to platter and rub with a garlic clove. Brush cut sides of romaine with reserved dressing; place half of romaine, cut side down, on grill. Grill, uncovered, until lightly charred (about one to two minutes). Move to platter with bread. Repeat.
5. Drizzle romaine with dressing and sprinkle with Parmesan cheese. Serve.