Combine flour, salt, cayenne, and black pepper in a zip-lock bag and mix until combined. Place the panko in a separate bag.
Using scissors, split the lobster tails, and remove the meat. Cut into bite-sized cubes. If the lobster meat is difficult to remove, blanch the lobster tails in boiling water for three minutes beforehand; cool quickly, and then extract the meat.
Place the eggs in a small bowl and whisk.
Add the lobster cubes into a plastic sealable bag, and shake to coat each piece.
Remove the lobster cubes from the bag. Dip the lobster into the egg mixture.
Place the coated lobster pieces directly into the bag with panko, shaking to coat. Set the lobster pieces aside on a plate in an even layer.
Add two inches of oil to a wide frying pan, turning the heat to medium-high. Once the pan is hot, turn down the temperature to medium, adding the breaded lobster in batches. Cook for one to two minutes until they are golden brown.
Remove the cooked pieces from the pan and place directly into a bowl with a paper towel lining the bottom.
Sprinkle the lobster with lime zest and a little extra salt and/or cayenne. Toss to coat.
Serve immediately with a lime wedge and dipping sauce of choice.