Whisk vinegar, lemon juice, garlic, mustard, sugar, 1/2 teaspoon kosher salt and black pepper (about 8 turns) together in a 2-cup measuring cup or small bowl.
Whisk in olive oil in a slow, steady steam to emulsify (combine as one).
Taste for seasoning and add more salt and pepper if necessary. (Remember that the cheese will add more saltiness too.)
This can be done ahead.
Combine lettuce, tomatoes (if using) and croutons in a salad bowl. Start with about half the dressing and add more as necessary. Mix in about 1/3 of the cheese. Divide among plates and top with the remaining parmesan.
Notes
Rinse and dry lettuce very well.Recommended: Fresh Gourmet Classic Caesar Croutons or Trader Joe's Garlic & Cheese Croutons Trader Joe's Extra Virgin California Estate Olive Oil Trader Joe's freshly grated Parmesan cheese