In a mixing bowl, combine crab meat, breadcrumbs, mayonnaise, Dijon mustard, beaten egg, lemon juice, Old Bay seasoning, parsley, salt, and pepper. Mix gently until well combined.
Shape the mixture into 8 patties and place them on a plate. Refrigerate for at least 30 minutes to help them firm up.
Heat olive oil in a frying pan over medium heat. Cook the crab cakes for 3-4 minutes on each side, or until golden brown and cooked through.
For the lemon aioli, combine mayonnaise, lemon juice, minced garlic, Dijon mustard, salt, and pepper in a small bowl. Mix until smooth.
Serve the crab cakes hot with a dollop of lemon aioli on top.