In a chilled mixing bowl, combine the aioli, the Parmesan, 2 tablespoons of warm water, and the garlic, using a rubber spatula or favorite wooden spoon. It's Caesar. Go old school.
Add the lemon juice progressively, not all at once. (Depending on the source and the season, lemons not only differ in size and the amount of juice inside, but also intensity.) Taste progressively, too. When you have a perfect balance of nutty Parmesan, pungent garlic, acid, and an almost-there salt level, it's right. And, it's up to you. Trust yourself.
Season with pepper and salt. Stir.
Chill, covered, until ready to serve.