In a medium bowl, coat the drained green olives with all-purpose flour.
Dip each flour-coated olive into the beaten eggs, then roll in a mixture of breadcrumbs, grated Parmesan, Italian seasoning, salt, and pepper. Place the breaded olives on a plate or baking sheet.
In a large skillet, heat vegetable oil over medium-high heat until it reaches 350°F.
Carefully add the breaded olives to the hot oil in batches, frying for 2-3 minutes or until golden brown and crispy. Use a slotted spoon to transfer the fried olives to a paper towel-lined plate to drain excess oil.
Repeat the frying process with the remaining olives.
While frying, prepare the garlic aioli. In a small bowl, mix mayonnaise, minced garlic, lemon juice, salt, and pepper until smooth and well combined.
Serve the fried olives hot with the garlic aioli for dipping.