Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C). Pat shrimp dry with paper towels.
Combine flour, lemon pepper seasoning, baking powder, salt, garlic powder, and cayenne together in a bowl. Whisk eggs and milk together in a second bowl.
Dip each shrimp in the egg mixture, then the flour mixture to evenly coat. Transfer prepared shrimp to a baking sheet until ready to fry. Sprinkle additional flour as needed to fully cover.
Cook 8 to 10 shrimp at a time in the hot oil until golden brown on the outside and cooked through on the inside, about 5 minutes. Transfer to a baking sheet lined with paper towels. Repeat with remaining shrimp.
Toss shrimp together with hot sauce in a large bowl until each piece is coated.