For the flatbread: Preheat the oven to 375 degrees F.
Brush two sheet pans with half the olive oil. Divide the naan between the sheet pans and brush the tops with the remaining olive oil. Toast in the oven until lightly brown and slightly crisp on the bottoms and around the edges, 10 to 12 minutes.
For the seafood sauce: Combine the mayonnaise, capers, parsley, salt, lemon zest and juice in a small bowl until smooth. Set aside.
For the crispy calamari: Heat 1 inch oil in a large pot to 375 degrees F.
Pat the calamari dry and set aside. Mix together the flour, seafood seasoning, salt and pepper in a shallow dish. Add the eggs and milk to a second shallow dish and mix together. Add the panko to a third shallow dish. Begin breading by dredging a few pieces of calamari in the seasoned flour, then dipping them in the egg mixture and then covering them in the panko. Set aside on a plate and repeat with the remaining calamari.
Fry the calamari in two batches, making sure to not overcrowd the pot, until golden and crisp, about 1 1/2 minutes. Remove to a paper towel-lined sheet pan and immediately squeeze a little lemon juice over the top; sprinkle with salt. Repeat with the remaining calamari.
Spread the sauce evenly across the top of each piece of naan, using a spoon to spread it almost to the edges. Sprinkle the lettuce over the sauce, then add the tomatoes and cucumbers. Generously top with the golden fried calamari. Sprinkle with hot sauce if desired, along with a squeeze of lemon and parsley. Serve with lemons wedges on the side.