Wipe mushrooms clean with a damp cloth. Remove stems and gills from mushrooms. Brush mushrooms lightly with olive oil. For a charcoal grill, grill mushrooms on the rack of an uncovered grill directly over medium coals for 5 minutes. Turn and grill 5 to 7 minutes more or until tender. (For a gas grill, preheat grill. Reduce heat to medium. Place mushrooms on grill rack over heat. Cover and grill as directed above.)
Meanwhile, in a small bowl, combine lemon juice, red wine vinegar, Dijon-style mustard, Worcestershire sauce, garlic, and pepper. Whisk in mayonnaise.
Slice grilled mushrooms. Toss lettuce with dressing in a very large bowl. Divide among serving plates. Top each with sliced mushrooms, croutons, and cheese.