Put the lemon juice in a small bowl. Using a microplane, grate the garlic into the lemon juice. Season with salt and pepper, and let sit 5-10 minutes (this will allow the garlic to mellow a bit). Whisk in the mayonnaise. Season with additional salt and pepper as needed.
Do Ahead: The aioli can be made up to 2 days in advance. Cover and store in the refrigerator.