Pulse the popcorn, panko, cornstarch, 1/2 teaspoon salt and a few grinds of black pepper in a food processor until coarsely ground. Transfer to a rimmed baking sheet. Combine the flour, 1/2 teaspoon salt and a few grinds of black pepper in a medium bowl; set aside. Beat the eggs in a separate bowl; set aside. Melt the butter with the cayenne, half of the lemon zest and a pinch of salt in a small saucepan; set aside.
Heat 2 inches vegetable oil in a large deep skillet or heavy-bottomed pot until a deep-fry thermometer registers 350 degrees F. Working in batches, toss the shrimp in the flour mixture until coated. Shake off the excess, then dip the shrimp in the eggs and let the excess drip off; coat in the popcorn mixture. Fry the shrimp until golden, about 2 minutes. Remove with a slotted spoon and transfer to a platter.
Mix the mayonnaise with the remaining lemon zest and the lemon juice. Drizzle the shrimp with the melted butter right before serving. Serve with the mayonnaise.