Remove rotisserie chicken from bones; then shred with 2 forks, or chop, until you have 3 cups of meat. If you have leftover chicken, reserve for another use.
In a large bowl, toss together lettuce, shredded chicken, grape tomatoes, and red onion.
For the dressing, mix the oil, lemon juice, white vinegar, anchovies (optional), garlic, dijon mustard, worcestershire sauce, egg yolks, and canned Parmesan cheese in the blender or food processor. Salt and pepper to taste. Chill dressing before using.
Before serving, pour the dressing over the salad. Drizzle balsamic vinegar over salad, squeeze 1/2 lemon, then gently toss to combine.
Sprinkle with fresh Parmesan cheese and croutons. Serve!