For the Calamari place the flour and Cajun spice mix in a large bowl and mix. Add the squid and turn until all the pieces are thoroughly coated. Shake off the excess mixture.
In a large, heavy pot or deep-fryer over medium heat, heat the oil to 375°F or until almost smoking.
Fry the squid for 2 to 3 minutes, or until a light golden brown.
Using a slotted spoon, transfer to paper towels to drain.
Serve immediately with lemon or lime wedges and Lemon Aioli.
For the Lemon Aioli place the zest, juice, mustard, garlic, egg yolks, pepper, salt, and bread in a blender or food processor and puree to a smooth paste.
With the machine running, drizzle in the oil. If the aioli appears too thick, add 2 tablespoons of water at a time to adjust the consistency. Store in an airtight jar in the refrigerator for up to 2 weeks.