In a blender, thoroughly combine the oil, vinegar, lemon juice, anchovies, garlic, and mustard.
Add the Parmesan and black pepper.
Blend until creamy and smooth.
Transfer to a small bowl and reserve, or, if made ahead, cover and refrigerate up to 3 days.
Whisk thoroughly before using.
Put the lettuce and croutons in a large salad bowl.
Add the dressing and toss well.