Make dip by combining first 5 ingredients in a small bowl. Refrigerate until needed. Preheat oven to 250˚F. Heat oil in your deep-fryer to 375°F. Line a large baking sheet with parchment paper. Place the buttermilk and flour in separate shallow bowls. Season the flour with salt and pepper.
Set the squid, lemon, squash and parsley in the buttermilk and toss well to ensure each item is coated. Working with a few pieces at a time, dredge the buttermilk coated items in the flour. As you go along, set the floured pieces, not touching if possible, on the baking sheet. Wash your hands.
Working in batches, shake excess flour off each coated item and then deep-fry until light golden and crisp, about 2 minutes. Drain on paper towels, and then keep warm in the oven on a clean baking sheet. Fry the rest of squid and other items in this fashion (see Note).
When all are cooked, arrange deep-fried items on a serving platter with the dip.
Note: Oblong delicata squash are available in our Produce Department. To prepare for this recipe, cut the squash in half lengthwise, remove the seeds and cut the amount required. Refrigerate and save the rest of the squash for another use. Before frying each batch of squid and other items, make sure the oil comes back up to 375˚F.