In a small steel bowl, add calamari (it should be very dry) and tempura batter; toss to coat. In a 350-degree fryer, drip an empty fry basket and slowly add calamari, being sure to separate each piece as it is gently placed in the grease. Fry until crisp but still tender inside, about 90 seconds.
In a steel bowl, combine arugula, calamari, salt, pepper, and dressing around the edge of the bowl; gently drag ingredients up and through dressing to evenly coat. Take half of the calamari and create a base for the salad. Then gently mound all of the arugula and the rest of the calamari on top of the base. Garnish with lemons and parsley.